Related papers: Rotating Wave Solutions to Lattice Dynamical Syste…
Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the…
The classical approach to linking lattice dynamics properties to continuum equations of motion, the "method of long waves," is extended to include higher order terms. The additional terms account for non-local and non-linear effects. In the…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
We study vortices in p-wave superconductors in a Ginzburg-Landau setting. The state of the superconductor is described by a pair of complex wave functions, and the p-wave symmetric energy functional couples these in both the kinetic…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
The existence of traveling front solutions to bistable lattice differential equations in the absence of a comparison principle is studied. The results are in the spirit of those in Bates, Chen, and Chmaj in[1], but are applicable to vector…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations. Small amplitude waves are studied within the linearization approximation…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators…
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local…
We consider several effects of the matter wave dynamics which can be observed in Bose-Einstein condensates embedded into optical lattices. For low-density condensates we derive approximate evolution equations, the form of which depends on…
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
The problem for two-dimensional steady water waves with vorticity is considered. Using methods of spatial dynamics, we reduce the problem to a finite dimensional Hamiltonian system. As an application, we prove the existence of non-symmetric…
This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…
The discrete complex Ginzburg-Landau equation is a fundamental model for the dynamics of nonlinear lattices incorporating competitive dissipation and energy gain effects. Such mechanisms are of particular importance for the study of…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the…
We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…