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#### Stability of bubble-like fluxons in disk-shaped Josephson junctions in the presence of a coaxial dipole current

ArticleJournal paper
Alicia G. Castro-Montes, Juan F. Marín, Diego Teca-Wellmann, Jorge A. González, and Mónica A. García-Ñustes
Chaos 30, 063132 (2020)
Publication year: 2020

#### Self-organization in the one-dimensional Landau–Lifshitz–Gilbert–Slonczewski equation with non-uniform anisotropy fields

Mónica A. García-Ñustes, Fernando R. Humire, Alejandro O. Leon
Publication year: 2020

In magnetic films driven by spin-polarized currents, the perpendicular-to-plane anisotropy is equivalent to breaking the time translation symmetry, i.e., to a parametric pumping. In this work, we numerically study those current-driven magnets via the Landau–Lifshitz– Gilbert–Slonczewski equation in one spatial dimension. We consider a space-dependent anisotropy field in the parametric-like regime. The anisotropy profile is antisymmetric to the middle point of the system. We find several dissipative states and dynamical behavior and focus on localized patterns that undergo oscillatory and phase instabilities. Using numerical simulations, we characterize the localized states’ bifurcations and present the corresponding diagram of phases.

#### Traveling wave into an unstable state in dissipative oscillator chains

ArticleJournal paper
Alfaro, Karin and Clerc, Marcel and Rojas, Rene and Garcia Ñustes, Monica
Alfaro, Karin & Clerc, Marcel & Rojas, Rene & Garcia Ñustes, Monica. (2019). Traveling wave into an unstable state in dissipative oscillator chains. Nonlinear Dynamics. 10.1007/s11071-019-05270-5.
Publication year: 2019

Coupled oscillators can exhibit complex spatiotemporal dynamics. Here, we study the propagation of nonlinear waves into an unstable state in dissipative coupled oscillators. To this, we consider the dissipative Frenkel–Kontorova model, which accounts for a chain of coupled pendulums or Josephson junctions and coupling superconducting quantum interference devices. As a function of the dissipation parameter, the front that links the stable and unstable state is characterized by having a transition from monotonous to non-monotonous profile. In the conservative limit, these traveling nonlinear waves are unstable as a consequence of the energy released in the propagation. Traveling waves into unstable states are peculiar of dissipative coupling systems. When the coupling and the dissipation parameter are increased, the average front speed decreases. Based on an averaging method, we analytically determine the front speed. Numerical simulations show a quite fair agreement with the theoretical predictions. To show that our results are generic, we analyze a chain of coupled logistic equations. This model presents the predicted dynamics, opening the door to investigate a wider class of systems.

#### Localized Faraday patterns under heterogeneous parametric excitation

ArticleJournal paper
Héctor Urra, Juan F. Marín, Milena Páez-Silva, Majid Taki, Saliya Coulibaly, Leonardo Gordillo, and Mónica A. García-Ñustes
PHYSICAL REVIEW E 99, 033115 (2019)
Publication year: 2019

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schrödinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.

#### Fate of the true-vacuum bubbles

ArticleJournal paper
Gonzalez J., Bellorín Alberto and Garcia Ñustes, Monica and Guerrero, Luis and Jiménez, Salvador and Marín, Juan and Vázquez, Luis
Journal of Cosmology and Astroparticle Physics 06(033) · June 2018
Publication year: 2018

We investigate the bounce solutions in vacuum decay problems. We show that it is possible to have a stable false vacuum in a potential that is unbounded from below.

#### Pi-kink propagation in the damped Frenkel-Kontorova model

ArticleJournal paper
Alfaro Karin, Clerc Marcel, Garcia Ñustes Monica, Rojas, Rene
EPL (Europhysics Letters) 119(4):40003
Publication year: 2017

Coupled dissipative nonlinear oscillators exhibit complex spatiotemporal dynamics. Frenkel-Kontorova is a prototype model of coupled nonlinear oscillators, which exhibits coexistence between stable and unstable state. This model accounts for several physical systems such as the movement of atoms in condensed matter and magnetic chains, dynamics of coupled pendulums, and phase dynamics between superconductors. Here, we investigate kinks propagation into an unstable state in the Frenkel-Kontorova model with dissipation. We show that unlike point-like particles ?-kinks spread in a pulsating manner. Using numerical simulations, we have characterized the shape of the ?-kink oscillation. Different parts of the front propagate with the same mean speed, oscillating with the same frequency but different amplitude. The asymptotic behavior of this propagation allows us to determine the minimum mean speed of fronts analytically as a function of the coupling constant. A generalization of the Peierls-Nabarro potential is introduced to obtain an effective continuous description of the system. Numerical simulations show quite fair agreement between the Frenkel-Kontorova model and the proposed continuous description.

#### Bubblelike structures generated by activation of internal shape modes in two-dimensional sine-Gordon line solitons

ArticleJournal paper
Garcia Ñustes Monica, Gonzalez J., Marín, Juan
Physical Review E 95(3):032222
Publication year: 2017

Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many impressive phenomena. In this work, we investigate a two-dimensional sine-Gordon model perturbed by a family of localized forces. We observed the formation of bubble-like and drop-like structures due to local internal shape modes instabilities. We describe the formation of such structures on the basis of a one-dimensional theory of activation of internal modes of sG solitons. An interpretation of the observed phenomena, in the context of phase transitions theory, is given. Implications on physical and biological systems are discussed.

#### Arbitrarily large numbers of kink internal modes in inhomogeneous sine-Gordon equations

ArticleJournal paper
Gonzalez J., Bellorín Alberto, Garcia Ñustes Monica, Guerrero Luis, Jiménez Salvador, Vázquez, L.
Physics Letters A volume 381 p. 1995
Publication year: 2017
We prove analytically the existence of an inﬁnite number of internal (shape) modes of sine-Gordon
solitons in the presence of some inhomogeneous long-range forces, provided some conditions are
satisﬁed.

#### An escape of vector matter-wave soliton from a parabolic trap

ArticleJournal paper
Bludov Yuliy, Garcia Ñustes Monica
Journal of Physics B Atomic Molecular and Optical Physics 50(13) ·
Publication year: 2017

We show that a vector matter-wave soliton in a Bose-Einstein condensate (BEC) loaded into an optical lattice can escape from a trap formed by a parabolic potential, resembling a Hawking emission. The particle-antiparticle pair is emulated by a low-amplitude bright-bright soliton in a two-component BEC with effective masses of opposite signs. It is shown that the parabolic potential leads to a spatial separation of BEC components. One component with chemical potential in a semi-infinite gap exerts periodical oscillations, while the other BEC component, with negative effective mass, escapes from the trap. The mechanism of atom transfer from one BEC component to another by spatially periodic linear coupling term is also discussed.

#### Front propagation into unstable states in discrete media

ArticleJournal paper
Alfaro-Bittner K., Clerc Marcel, Garcia Ñustes Monica, Rojas, Rene
Publication year: 2016

Non-equilibrium dissipative systems usually exhibit multistability, leading to the presence of propagative domain between steady states. We investigate the front propagation into an unstable state in discrete media. Based on a paradigmatic model of coupled chain of oscillators and populations dynamics, we calculate analytically the average speed of these fronts and characterize numerically the oscillatory front propagation. We reveal that different parts of the front oscillate with the same frequency but with different amplitude. To describe this latter phenomenon we generalize the notion of the Peierls-Nabarro potential, achieving an effective continuous description of the discreteness effect.

#### Chimera-type states induced by local coupling

ArticleJournal paper
Clerc Marcel, Coulibaly Saliya, Ferré Michel, Garcia Ñustes Monica, Rojas, Rene
PHYSICAL REVIEW E 93(5) · May 2016
Publication year: 2016

Coupled oscillators can exhibit complex self-organization behavior such as phase turbulence, spatiotemporal intermittency, and chimera states. The latter corresponds to a coexistence of coherent and incoherent states apparently promoted by nonlocal or global coupling. Here we investigate the existence, stability properties, and bifurcation diagram of chimera-type states in a system with local coupling without different time scales. Based on a model of a chain of nonlinear oscillators coupled to adjacent neighbors, we identify the required attributes to observe these states: local coupling and bistability between a stationary and an oscillatory state close to a homoclinic bifurcation. The local coupling prevents the incoherent state from invading the coherent one, allowing concurrently the existence of a family of chimera states, which are organized by a homoclinic snaking bifurcation diagram.

#### Transverse phase shielding solitons in the degenerated optical parametric oscillator

ArticleJournal paper
Clerc Marcel, Coulibaly Saliya, Garcia Ñustes Monica, Zárate, Yair}
Optics Communications 354 · November 2015
Publication year: 2015

#### Recurrent noise-induced phase singularities in drifting patterns

ArticleJournal paper
Clerc Marcel, Coulibaly Saliya, Campo F, Garcia Ñustes Monica, Louvergneaux E., Wilson Mario
Physical Review E 92(5):50902(R)
Publication year: 2015

We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.

#### Noise-induced traveling Nozaki-Bekki holes and vortices in experimental drifting patterns

Conference paper
Clerc Marcel, Coulibaly Saliya, Campo Francisco, Garcia Ñustes Monica, Louvergneaux E.,Wilson Mario
Conference: Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides
Publication year: 2014

We show that, in drifting systems, noise is responsible for inducing permanent traveling phase singularities by generating specific initial conditions Experimentally, these defects are evidenced in a Kerr medium submitted to a tilted optical feedback

#### Hawking-like escape of the soliton from the trap in two-component Bose-Einstein condensate

ArticleJournal paper
Bludov, Yuliy, Garcia Ñustes Monica
Publication year: 2014

We demonstrate, that Bose-Einstein condensate can escape from the trap, formed of combined linear periodic (optical lattice) and parabolic potentials, and the escaping mechanism is similar to Hawking radiation from black hole. The low-amplitude bright-bright soliton in two-component Bose-Einstein condensate (where chemical potentials of the BEC first and second components are located nearby the opposite edges of the first band of the optical lattice spectrum) serves as an analogue of particle-antiparticle pair in Hawking radiation. It is shown that parabolic potential, being applied to such two-component BEC, leads to spatial separation of its components: BEC component with chemical potential located in semi-infinite gap exerts the periodical oscillations, while the BEC component, whose chemical potential is in the first finite gap, escapes from the trap (due to negative effective mass of gap soliton). We also propose a method for the creation of such bright-bright soliton — transferring of atoms from one BEC component to another by spatially periodic linear coupling term.

#### Formation and Interaction of Two-Kink Solitons

Book Chapter
Garcia Ñustes Monica
Hyper-Chaotic and Chaotic Synchronisation of Two Interacting Dipoles
Publication year: 2014

Two-kink soliton solutions have received attention due to its implications in string theory and particles physics. In the present work we analyze the necessary conditions for the appearance of two-kink solitons in the sine-Gordon model under the perturbation of a space-dependant force. Interactions of two-kink solitons are also investigated. We show that kink repulsive force eventually leads to a fragmentation of the solution before interaction and finally to dissolution of these bound states.

#### Emergence of spatiotemporal dislocation chains in drifting patterns

ArticleJournal paper
Clerc, Marcel, Falcón Claudio, Garcia Ñustes Monica, Odent Vincent, Ortega I.
Chaos (Woodbury, N.Y.) 24(2):023133
Publication year: 2014

One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and complex spatiotemporal dynamics, which is characterized by the perpetual emergence of spatiotemporal dislocation chains. Using a universal amplitude equation of drifting patterns, we show that this behavior is a result of a combination of a phase instability and an advection process caused by an inhomogeneous drift force. The emergence of spatiotemporal dislocation chains is verified in numerical simulations on an optical feedback system with a non-uniform intensity pump. Experimentally this phenomenon is also observed in a tilted quasi-one-dimensional fluidized shallow granular bed mechanically driven by a harmonic vertical vibration.

#### Dissipation-Driven Behavior of Nonpropagating Hydrodynamic Solitons Under Confinement

ArticleJournal paper
Gordillo, Leonardo, Garcia Ñustes, Monica
Physical Review Letters 112(16):164101
Publication year: 2014

We have identified a physical mechanism that rules the confinement of nonpropagating hydrodynamic solitons. We show that thin boundary layers arising on walls are responsible for a jump in the local damping. The outcome is a weak dissipation-driven repulsion that determines decisively the solitons’ long-time behavior. Numerical simulations of our model are consistent with experiments. Our results uncover how confinement can generate a localized distribution of dissipation in out-of-equilibrium systems. Moreover, they show the preponderance of such a subtle effect in the behavior of localized structures. The reported results should explain the dynamic behavior of other confined dissipative systems.

#### Spatially modulated kinks in shallow granular layers

ArticleJournal paper
Macías J, Clerc Marcel, Falcón Claudio, Garcia Ñustes, Monica
Physical Review E 88(2):020201
Publication year: 2013

We report on the experimental observation of spatially modulated kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow. We show the appearance of these solutions as the layer undergoes a parametric instability. Due to the inherent fluctuations of the granular layer, the kink profile exhibits an effective wavelength, a precursor, which modulates spatially the homogeneous states and drastically modifies the kink dynamics. We characterize the average and fluctuating properties of this solution. Finally, we show that the temporal evolution of these kinks is dominated by a hopping dynamics, related directly to the underlying spatial structure.

#### Propagative phase shielding solitons in inhomogeneous media

Clerc Marcel, Garcia Ñustes Monica, Zárate, Yair
Physica D: Nonlinear Phenomena Volume 269, 15 February 2014, Pages 86-93
Publication year: 2013

Dissipative solitons in parametrically driven systems propagating in a spatial inhomogeneous medium are investigated. Recently, a family of dissipative solitons with an unexpected shell-type phase structure has been reported. In the present work, we show that the phase configuration moves rigidly along with the modulus after some transient state. Such a transient state is characterized for a self-adaptation of the phase front symmetry and its relative distance to the soliton. The described dynamical behavior is analytically predicted, showing good agreement with numerical simulations. A mechanism of control and manipulation of these structures based on spatial inhomogeneities is proposed.

#### Phase shielding soliton in parametrically driven systems

ArticleJournal paper
Clerc Marcel, Garcia Ñustes Monica, Zárate, Yair, Coulibaly, Saliya
Physical Review E 87(5-1):052915
Publication year: 2013

Parametrically driven extended systems exhibit dissipative localized states. Analytical solutions of these states are characterized by a uniform phase and a bell-shaped modulus. Recently, a type of dissipative localized state with a nonuniform phase structure has been reported: the phase shielding solitons. Using the parametrically driven and damped nonlinear Schrödinger equation, we investigate the main properties of this kind of solution in one and two dimensions and develop an analytical description for its structure and dynamics. Numerical simulations are consistent with our analytical results, showing good agreement. A numerical exploration conducted in an anisotropic ferromagnetic system in one and two dimensions indicates the presence of phase shielding solitons. The structure of these dissipative solitons is well described also by our analytical results. The presence of corrective higher-order terms is relevant in the description of the observed phase dynamical behavior.

#### Publisher’s Note: Origin of the Pinning of Drifting Monostable Patterns [Phys. Rev. Lett. 109, 104101 (2012)]

Clerc Marcel, Fernandez-Oto Cristian, Garcia Ñustes Monica Louvergneaux, E.
Physical Review Letters 109(12) · September 2012
Publication year: 2012

#### Origin of the Pinning of Drifting Monostable Patterns

ArticleJournal paper
Clerc Marcel, Fernandez-Oto Cristian, Garcia Ñustes, Monica, Louvergneaux, E.
Physical Review Letters 109(10):104101
Publication year: 2012

Under drift forces, a monostable pattern propagates. However, examples of nonpropagative dynamics have been observed. We show that the origin of this pinning effect comes from the coupling between the slow scale of the envelope to the fast scale of the modulation of the underlying pattern. We evidence that this effect stems from spatial inhomogeneities in the system. Experiments and numerics on drifting pattern-forming systems subjected to inhomogeneous spatial pumping or boundary conditions confirm this origin of pinning dynamics.

#### Formation of a two-kink soliton pair in perturbed sine-Gordon models due to kink–internal-mode instabilities

ArticleJournal paper
Garcia Ñustes Monica, Gonzalez, J.
Physical Review E 86(6-2):066602
Publication year: 2012

The existence of two-kink soliton solutions in polynomial potentials was first reported by Bazeia et al. in a special type of scalar field systems [Phys. Rev. Lett. 91, 241601 (2003)]. A general feature of these potentials is that they possess two minima and a local metastable minimum between them. In the present work we investigate the appearance of this special kind of soliton in the sine-Gordon model under the perturbation of a space-dependent force. We show that a pair of solitons is emitted during the process of kink breakup by internal mode instabilities. A possible explanation of these phenomena is an interplay between the solitons repelling interaction and the external force, resulting in a separation or a packing of several kinks.

#### Dissipative Localized States with Shieldlike Phase Structure

ArticleJournal paper
Clerc Marcel, Coulibaly, Saliya, Garcia Ñustes Monica, Zárate Yair
Physical Review Letters 107(25):254102 · December 2011
Publication year: 2011

A novel type of parametrically excited dissipative solitons is unveiled. It differs from the well-known solitons with constant phase by an intrinsically dynamical evolving shell-type phase front. Analytical and numerical characterizations are proposed, displaying quite a good agreement. In one spatial dimension, the system shows three types of stationary solitons with shell-like structure whereas in two spatial dimensions it displays only one, characterized by a π-phase jump far from the soliton position.

#### Kink propagation in inhomogeneous systems driven by spatiotemporal perturbations

ArticleJournal paper
Garcia Ñustes Monica, Rondón I., Gonzalez, J., Chacón, Ricardo
Journal of Physics Conference Series 246(1):012008 · September 2010
Publication year: 2010

We investigate the propagation of kinks in inhomogeneous media. We show that the extended character of the kink, the internal mode instabilities and the phenomenon of disappearance of the translational mode can affect the kink motion in the presence of space-dependent external perturbations. We apply the results to the analysis of kink ratchets and the propagation of kinks driven by wave fields.

#### Universal functions and exactly solvable chaotic systems

ArticleJournal paper
Garcia Ñustes, Monica and Hernandez-Garcia, Emilio and Gonzalez, J.
10.11606/issn.2316-9028.v2i2p204-221
Publication year: 2008

A universal differential equation is a nontrivial differential equation the solutions of which approximate to arbitrary accuracy any continuous function on any interval of the real line. On the other hand, there has been much interest in exactly solvable chaotic maps. An important problem is to generalize these results to continuous systems. Theoretical analysis would allow us to prove theorems about these systems and predict new phenomena. In the present paper we discuss the concept of universal functions and their relevance to the theory of universal differential equations. We present a connection between universal functions and solutions to chaotic systems. We will show the statistical independence between $X(t)$ and $X(t + \tau)$ (when $\tau$ is not equal to zero) and $X(t)$ is a solution to some chaotic systems. We will construct universal functions that behave as delta-correlated noise. We will construct universal dynamical systems with truly noisy solutions. We will discuss physically realizable dynamical systems with universal-like properties.

#### Statistical Independence in Nonlinear Maps Coupled to Non-invertible Transformations

ArticleJournal paper
Wang, Kai and Xia, Haishan and Garcia Ñustes, Monica and Gonzalez, J.
Physics Letters A 372:6593 - 6601 · October 2008
Publication year: 2008

We investigate the connections between functions of type x(n) = p(theta Tz(n)) and nonlinear maps coupled to non-invertible transformations. These systems can produce unpredictable dynamics. We study the higher-order correlations in the generated sequences. We show that (theoretically) it is possible to construct systems that can generate sequences that constitute a set of statistically independent random variables. We apply the results in the improvement of a two-dimensional coupled map system that has been used in practical applications as e.g. cryptosystems and data compression.

#### Hawking-like emission in kink-soliton escape from a potential well

ArticleJournal paper
Gonzalez, J., Garcia Ñustes, Monica, Sánchez, Angel, McClintock, P
New Journal of Physics 10 (2008) 113015 (19pp)
Publication year: 2008

The escape of solitons over a potential barrier is analysed within the framework of a nonlinear Klein-Gordon equation. It is shown that the creation of a kink-antikink pair near the barrier through an internal mode instability can be followed by escape of the kink in a process analogous to Hawking radiation. These results have important implications in a wider context, including stochastic resonance and ratchet systems, which are also discussed.

#### A recipe for an unpredictable random number generator

ArticleJournal paper
Garcia Ñustes, Monica and Trujillo, Leonardo and Gonzalez, J.
Condensed Matter Physics 9(2) · June 2006
Publication year: 2006
In this work we present a model for computation of random processes in digital
computers which solves the problem of periodic sequences and hidden errors pro-
duced by correlations. We show that systems with non-invertible non-linearities can
produce unpredictable sequences of independent random numbers. We illustrate our
result with some numerical calculations related with random walks simulations