Related papers: Separability in 1+1 Dimensions in Classical Nonlin…
We present a first-principles derivation of the variational equations describing the dynamics of the interaction of a spatial soliton and a surface plasmon polariton (SPP) propagating along a metal/dielectric interface. The variational…
Although extreme or freak waves are repeatedly measured in the oceans, their origin is largely unknown. The interaction of different water waves is seen as one reason for their emergence. One way to consider nonlinear waves in deep water is…
We consider the Adlam-Allen (AA) system of partial differential equations which, arguably, is the first model that was introduced to describe solitary waves in the context of propagation of hydrodynamic disturbances in collisionless…
We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of breathers with high power. Three main regimes are observed:…
Solitary electromagnetic waves propagating along the waveguides forming a rhombic one-dimensional lattice are considered. Two waveguides that are part of the unit cell are assumed to be made of an optical linear material, while the third…
We study the existence of solitary-wave solutions and some of their properties for a general multicomponent long-wave-short-wave interaction system. The system considered here describes the nonlinear interaction of multiple short waves with…
We consider a system of coupled nonlinear Schr{\"o}dinger equations in one space dimension. First, we prove the existence of multi-speed solitary waves, i.e solutions to the system with each component behaving at large times as a solitary…
We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type…
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. A soliton is a solitary wave which exhibits some strong form of stability so that…
Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in $1+1$ dimensions. There are three different topological soliton solutions which be labelled according to their topological…
In recent years, bright soliton-like structures composed of gaseous Bose-Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced…
The interaction between two parallel beams in one-dimensional discrete saturable systems has been investigated using lithium niobate nonlinear waveguide arrays. When the beams are separated by one channel and in-phase it is possible to…
We consider the nonlinear Klein-Gordon equation in $\R^d$. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the…
Solitons are commonly known as waves that propagate without dispersion. Here we show that they can occur for driven overdamped Brownian dynamics of hard spheres in periodic potentials at high densities. The solitons manifest themselves as…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…
In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and…
Soliton molecules, bound states of two solitons, can be important for the informatics using solitons and the quest for exotic particles in a wide range of physical systems from unconventional superconductors to nuclear matter and Higgs…
The paper addresses the bistability caused by spontaneous symmetry breaking bifurcation in a one-dimensional periodically corrugated nonlinear waveguide pumped by coherent light at normal incidence. The formation and the stability of the…
Solitons in nematic liquid crystals offer intriguing opportunities for transport and sensing in microfluidic systems. Little is known about the elementary conditions that are needed to create solitons in nematic materials. In this work,…
In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one components, namely interlaced solitons. These are waveforms in which in the relevant anti-continuum limit, i.e.…