Related papers: The Nikolaevskiy equation with dispersion
The stochastic Gross-Pitaevskii equation represents a versatile approach for studying the dynamics of trapped degenerate ultracold Bose gases in the presence of large phase and density fluctuations. Following a brief review of the original…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
The multiscaling properties of the mixed Obukhov-Novikov shell model of turbulence are investigated numerically and compared with those of the complex GOY model, mostly studied in the recent years. Two types of generic singular fluctuations…
A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
For Nicholson's blowflies equation, a kind of reaction-diffusion equations with time-delay, when the ratio of birth rate coefficient and death rate coefficient satisfies $\frac{p}{\delta}>e$, the large time-delay $r>0$ usually causes the…
The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational case. Moreover we give necessary conditions for the existence of partially and totally…
Wave turbulence is the study of the long-time statistical behaviour of equations describing a set of weakly non-linear interacting waves. Such a theory, which has a natural asymptotic closure, allows us to probe the nature of turbulence…
We propose a methodology for designing well-balanced numerical schemes to investigate traveling waves in parabolic models from mathematical biology. We combine well-balanced techniques for parabolic models known in the literature with the…
Theory of laminated turbulnece includes continuous layer of turbulence (statistical description, kinetic equations, Zakharov-Kolmogorov spectra, etc) AND discrete layer of turbulence (isolated groups of interacting waves, no…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
The Enskog--Vlasov (EV) equation is a semi-empiric kinetic model describing gas-liquid phase transitions. In the framework of the EV equation, these correspond to an instability with respect to infinitely long perturbations, developing in a…
The FitzHugh-Nagumo equation, which was derived as a simplification of the Hodgkin-Huxley model for nerve impulse propagation, has been extensively studied as a paradigmatic activator-inhibitor system. We consider the version of this system…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
In field theory, particles are waves or excitations that propagate on the fundamental state. In experiments or cosmological models one typically wants to compute the out-of-equilibrium evolution of a given initial distribution of such…
In this paper, we address the stability of transport systems and wave propagation on networks with time-varying parameters. We do so by reformulating these systems as non-autonomous difference equations and by providing a suitable…
Second-order macroscopic continuum models have been constantly improving for decades to reproduce the empirical observations. Recently, a series of experimental studies have suggested that the stochastic factors contribute significantly to…
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…
Partial differential equations endowed with a Hamiltonian structure, like the Korteweg--de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for…