Related papers: Travelling Wave Solutions in Nonlinear Diffusive a…
The article produces a brief review of some recent results which predict stable propagation of solitons and solitary vortices in models based on the nonlinear Schroedinger equation including fractional one- or two-dimensional diffraction…
Using the Darboux transformation for the Korteweg-de Vries equation, we construct and analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal wave. Due to their unsteady, wavepacket-like character,…
In this study, we investigate a porous medium-type flux limited reaction--diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized…
We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
We first point out it is conditional to apply the variational approach to the nonlocal nonlinear Schr\"{o}dinger equation (NNLSE), that is, the response function must be an even function. Different from the variational approach, the…
The goal of this note is to construct a class of traveling solitary wave solutions for the compound Burgers-Korteweg-de Vries equation by means of a hyperbolic ansatz.
The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…
We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions…
We theoretically investigate the properties of phonon-polariton inhomogeneous harmonic wave, cnoidal wave and spatial soliton propagating in boundless dielectric medium and compute the shape of nonlinear vector polariton wave. We obtain…
The effects of the non-extensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics with the non-extensive equation of state. We have shown that…
We study long nonlinear longitudinal bulk strain waves in a hyperelastic rod of circular cross section within the scope of the general weakly-nonlinear elasticity leading to a model with quadratic and cubic nonlinearities. We systematically…
We examine the possibility of travelling wave solutions within the nonlinear Euler-Heisenberg electrodynamics. Since this theory resembles in its form the electrodynamics in matter, it is a priori not clear if there exist travelling wave…
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, discrete, homogeneous chains with a general power-law contact interaction is studied. For this wave equation,…
We study the modulated Korteweg-de~Vries equation (KdV) on the circle with a time non-homogeneous modulation acting on the linear dispersion term. By adapting the normal form approach to the modulated setting, we prove sharp unconditional…
In this paper, we employ a combination of analytical and numerical techniques to investigate the dynamics of lattice envelope vector soliton solutions propagating within a one-dimensional chain of flexible mechanical metamaterial. To model…
In this paper we present a rigorous modulational stability theory for periodic traveling wave solutions to equations of nonlinear Schr\"odinger (NLS) type. We first argue that, for Hamiltonian dispersive equations with a non-singular…
We demonstrate that families of vortex solitons are possible in a bi-dispersive three-dimensional nonlinear Schrodinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third…
Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…