Related papers: Nonlinear wave interactions for the Benjamin-Ono e…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that…
We address the properties of surface-wave solitons on the interface between a semi-infinite homogeneous linear medium and a semi-infinite homogeneous nonlinear nonlocal medium. The stability, energy flow and FWHM of the surface wave…
We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDE of KdV-type, including generalized KdV and Benjamin-Ono equations. In this investigation, we consider the…
The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow…
We adapt the microcanonical framework of equilibrium statistical mechanics to predict the statistics of short waves in inhomogeneous moving media. For steady inhomogeneities and background flow, we compute the wave spectrum at any location…
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
We consider the stability and instability of periodic travling waves for Korteweg-de Vries type equations with fractional dispersion and other nonlinear dispersive equations. We establish that a constrained minimizer for the related…
We have shown that the wave scattering by a soliton occurs in a peculiar way. The nonlinear interaction leads to the generation of waves with frequencies that are multiples of the frequency of the incident wave, minus the frequency of the…
We use Wasserstein metrics adapted to study the action of the flow of the BBM equation on probability measures. We prove the continuity of this flow and the stability of invariant measures for finite times.
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
We investigate self-interacting scalar, pseudoscalar and vector meson fields and their influence on NN interactions. Due to the self--interaction one has to solve nonlinear field equations which allow solitary wave solutions. A propability…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
Positive and negative ions forming so-called pair plasma differing in sign of their charge and asymmetric in mass and temperature support a new electrostatic mode. Bernstein mode for a pair ions and pair ions with contribution of electrons…
The numerical simulation of the nonlinear dynamics of random sea waves at moderately small Benjamin-Feir indices and its comparison with the linear dynamics (at the coincidence of spatial Fourier harmonics near a spectral peak at a certain…
In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution…
In this paper we present an experimental study of the long surface wave instability that can develop when a granular material flows down a rough inclined plane. The threshold and the dispersion relation of the instability are precisely…
We consider a one-dimensional partial differential equation system modeling heat flow around a ring. The system includes a Klein-Gordon wave equation for a field satisfying spatial periodic boundary conditions, as well as Ornstein-Uhlenbeck…
We investigate the Benjamin-Feir (or modulational) instability of Stokes waves, i.e., small-amplitude, one-dimensional periodic gravity waves of permanent form and constant velocity, in water of finite and infinite depth. We develop a…