Related papers: Soliton dynamics in symmetric and non-symmetric co…
Soliton rate equations are based on non-Kolmogorovian models of probability and naturally include autocatalytic processes. The formalism is not widely known but has great unexplored potential for applications to systems interacting with…
We study the excitation, decay and interactions of novel, velocity locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We analytically describe the particle-like scattering between stable or…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…
We investigate the soliton dynamics for the Schrodinger-Newton system by proving a suitable modulational stability estimates in the spirit of those obtained by Weinstein for local equations.
This paper studies the behavior of solitons in the Korteweg-de Vries equation under the influence of multiplicative noise. We introduce stochastic processes that track the amplitude and position of solitons based on a rescaled frame…
A numerical fluid simulation investigation of the temporal evolution of a special class of traveling wave solution of the one dimensional relativistic cold plasma model is reported.The solutions consist of coupled electromagnetic and plasma…
Recent highly idealized model studies of lubricated nanofriction for two crystalline sliding surfaces with an interposed thin solid crystalline lubricant layer showed that the overall relative velocity of the lubricant $v_{\rm lub} / v_{\rm…
Dynamics of solitons is considered in the framework of the extended nonlinear Schrodinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the…
We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocing cross-interactions. The general properties of the stationary states and their stability are investigated. The different scenarios…
Physics students now have access to interactive molecular dynamics simulations that can model and animate the motions of hundreds of particles, such as noble gas atoms, that attract each other weakly at short distances but repel strongly…
The motion of three-dimensional (3D) solitary waves and solitons in nonlinear crystal-like structures, such as photonic materials, is studied. It is demonstrated that collective excitations in these systems can be tailored to move in…
Solitons, as coherent structures that maintain their shape while traveling at constant velocity, are ubiquitous across various branches of physics, from fluid dynamics to quantum fields. However, it is within the realm of optics where…
Considering a periodically oscillating harmonic potential, we explore the dynamics properties of bright solitons in a Bose-Einstein condensate. It is found that under a slower oscillating potential, soliton movement exhibits a nonperiodic…
We have considered relativistic soliton dynamics governed by the sine-Gordon equation and affected by short spatial inhomogeneities of the driving force and thermal noise. Developed analytical and numerical methods for calculation of…
In this paper, we study the competition of linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian…
Transport processes in crowded periodic structures are often mediated by cooperative movements of particles forming clusters. Recent theoretical and experimental studies of driven Brownian motion of hard spheres showed that cluster-mediated…
In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive,…
We present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some wide assumptions, we show the joint distribution of the position…
Consider a branch of unstable solitons of NLS whose linearized operators have one pair of simple real eigenvalues in addition to the zero eigenvalue. Under radial symmetry and standard assumptions, solutions to initial data from a…