84 research outputs found
Discrete breathers collisions: An overview and some recent results
We present some results on breather collisions in DNLS lattices, with special focus on systems with saturable nonlinearity. We also review some other works concerning to collisons in FPU and Klein-Gordon lattices, proposing future challenges
Solitons for the cubic-quintic nonlinear Schrödinger equation with time and space modulated coefficients
In this paper, we construct, by means of similarity transformations, explicit solutions to the cubic–quintic nonlinear Schrödinger equation with potentials and nonlinearities depending on both time and spatial coordinates. We present the general approach and use it to calculate bright and dark soliton solutions for nonlinearities and potentials of physical interest in applications to Bose–Einstein condensates and nonlinear optics.project FIS2008-02873 Ministerio de Ciencia e Innovació
Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotics
In this paper, we give a proof of the existence of stationary dark solitonsolutions or heteroclinic orbits of nonlinear equations of Schrödinger type with periodic inhomogeneous nonlinearity. The result is illustrated with examples of dark solitons for cubic and photorefractive nonlinearities.MICINN project FIS2008-0484
Ratchet effect in solids: Defect transport driven by biharmonic forces
PósterInterstitials and vacancies, in one-dimensional lattices, are
point defects that can be modelled by means of kinks or antikinks in a
discrete Frenkel-Kontorova model, with a sine-Gordon on-site potential.
The properties of kinks and antikinks are the same if a harmonic interaction
potential is considered. The ratchet properties of these defects in
the above mentioned context has been studied by Zolotaryuk and Salerno
when the system is driven by a biharmonic field. The properties of these
solutions are strongly altered when an anharmonic interaction potential
is introduced in the model, as the Peierls-Nabarro barrier is higher for
antikinks than for kinks. The aim of this poster is to show the effects of
the anharmoniciy of the interaction potential in the properties of kinks
and antikinks focusing in the assymetry between the properties of these
two species of topological solitonsMinisterio de Educación y Ciencia FIS2006-27277-
An energy-based stability criterion for solitary traveling waves in Hamiltonian lattices
In this work, we revisit a criterion, originally proposed in [Nonlinearity
{\bf 17}, 207 (2004)], for the stability of solitary traveling waves in
Hamiltonian, infinite-dimensional lattice dynamical systems. We discuss the
implications of this criterion from the point of view of stability theory, both
at the level of the spectral analysis of the advance-delay differential
equations in the co-traveling frame, as well as at that of the Floquet problem
arising when considering the traveling wave as a periodic orbit modulo a shift.
We establish the correspondence of these perspectives for the pertinent
eigenvalue and Floquet multiplier and provide explicit expressions for their
dependence on the velocity of the traveling wave in the vicinity of the
critical point. Numerical results are used to corroborate the relevant
predictions in two different models, where the stability may change twice. Some
extensions, generalizations and future directions of this investigation are
also discussed
A PT-Symmetric Dual-Core System With the Sine-Gordon Nonlinearity and Derivative Coupling
We propose a system of sine-Gordon equations, with the symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in the coupled Frenkel-Kontorova (FK) chains and related sine-lattices, while the cross-derivative coupling, which was not considered before, is induced by \emph{three-particle} interactions, provided that the particles in the parallel FK\ chains move in different directions. Nonlinear wave structures are then studied in this model. In particular, kink-kink (KK) and kink-antikink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling, and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks/antikinks that may propagate or become stationary, depending on whether they are subject to gain or loss, respectively
Nonlinearity and Topology
The interplay of nonlinearity and topology results in many novel and
emergent properties across a number of physical systems such as chiral magnets,
nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics,
etc. It also results in a wide variety of topological defects such as solitons, vortices,
skyrmions, merons, hopfions, monopoles to name just a few. Interaction among
and collision of these nontrivial defects itself is a topic of great interest. Curvature
and underlying geometry also affect the shape, interaction and behavior of these
defects. Such properties can be studied using techniques such as, e.g. the Bogomolnyi
decomposition. Some applications of this interplay, e.g. in nonreciprocal photonics as
well as topological materials such as Dirac andWeyl semimetals, are also elucidated.AEI/FEDER, (UE) MAT2016-79866-
The closeness of the Ablowitz-Ladik lattice to the Discrete Nonlinear Schrödinger equation
While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schrödinger equation, which is more significant for physical applications, is not. We prove closeness of the solutions of both systems in the sense of a “continuous dependence” on their initial data in the and metrics. The most striking relevance of the analytical results is that small amplitude solutions of the Ablowitz-Ladik system persist in the Discrete Nonlinear Schrödinger one. It is shown that the closeness results are also valid in higher dimensional lattices, as well as, for generalised nonlinearities. For illustration of the applicability of the approach, a brief numerical study is included, showing that when the 1-soliton solution of the Ablowitz-Ladik system is initiated in the Discrete Nonlinear Schrödinger system with cubic or saturable nonlinearity, it persists for long-times. Thereby, excellent agreement of the numerical findings with the theoretical predictions is obtained.Regional Government of Andalusia and EU (FEDER program) project P18-RT-3480Regional Government of Andalusia and EU (FEDER program) project US-1380977MICINN, AEI and EU (FEDER program) project PID2019-110430GB-C21MICINN, AEI and EU (FEDER program) project PID2020-112620GB-I0
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