Related papers: Travelling waves in nonlinear magneto-inductive la…
The discrete periodic lattice of masses and springs with line and point defects is considered. The dispersion equations for propagative, guided and localised waves are obtained. The detailed analysis of example with three masses is…
New travelling wave solutions to the Fornberg-Whitham equation are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.
We study the Muskat problem for one fluid in arbitrary dimension, bounded below by a flat bed and above by a free boundary given as a graph. In addition to a fixed uniform gravitational field, the fluid is acted upon by a generic force…
We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii…
We study the dispersion of electromagnetic waves in a spatially dispersive metamaterial with Lorentz-like dependence of principal permittivity tensor components on the respective components of the wave vector performing the analysis of…
We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R} $$ satisfying Maxwell's equations in a nonlinear medium which is not necessarily…
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…
The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in…
In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of…
Propagation of transition fronts in models of coupled oscillators with non-degenerate on-site potential is usually considered in terms of travelling waves. We show that the system dynamics can be reformulated as an implicit map structure,…
The interaction of the nonlinear internal waves with a nonuniform current with a specific form, characteristic for the equatorial undercurrent, is studied. The current has no vorticity in the layer, where the internal wave motion takes…
A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi…
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…
We investigate the existence of periodic trajectories of a particle, subject to a central force, which can hit a sphere, or a cylinder. We will provide also a Landesman-Lazer type of condition in the case of a nonlinearity satisfying a…
It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…
We prove the existence of small-amplitude periodic traveling waves in dimer Fermi-Pasta-Ulam-Tsingou (FPUT) lattices without assumptions of physical symmetry. Such lattices are infinite, one-dimensional chains of coupled particles in which…
In this paper we study the isolated periodic traveling wave solutions of a family of reaction-convection-diffusion equations with cubic reaction term. Existence/nonexistence of periodic traveling wave solutions are discussed in different…
Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations…
The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic…