Related papers: On short wave-long wave interactions in the relati…

A space discretization of an integrable long wave-short wave interaction model, called the Yajima-Oikawa system, was proposed in the recent paper arXiv:1509.06996 using the Hirota bilinear method (see also…

We study here the propagation of long waves in the presence of vorticity. In the irrotational framework, the Green-Naghdi equations (also called Serre or fully nonlinear Boussinesq equations) are the standard model for the propagation of…

Using a two-fluid approach, we consider the properties of relativistically nonlinear (arbitrary $a_0$), circularly polarized \EM\ waves propagating along magnetic field in electron-ion and pair plasmas. Dispersion relations depend on how…

The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…

We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the…

Lorentz scalar and mass interactions are studied in more detail in the framework of a reduced Dirac equation for heavy quark-antiquark mesons. A microscopic model for these interactions is proposed and analyzed. The charmonium mass spectrum…

The recent observation of gravitational waves, stimulates the question of the longtime evolution of the space-time fluctuations. Gravitational waves interact themselves through the nonlinear character of Einstein's equations of general…

Starting from the two-dimensional Boussinesq equation without rotation, we derive a kinetic equation for weak interaction of internal waves using non-canonical variables. We follow a formalism introduced by P. Ripa in the 80's. The…

The Hirota equation is a higher order extension of the nonlinear Schroedinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of…

We show that a nonlinear Schr\"odinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory…

We study the permanent regimes of the reduced Vlasov-Maxwell system for laser-plasma interaction. A non-relativistic and two different relativistic models are investigated. We prove the existence of solutions where the distribution function…

Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a…

It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear…

Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…

The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The…

Recent work has given a systematic way for studying the kinetics of classical weakly interacting waves beyond leading order, having analogies with renormalization in quantum field theory. An important context is weak wave turbulence,…

We study an example of exact parametric resonance in a extended system ruled by nonlinear partial differential equations of nonlinear Schr\"odinger type. It is also conjectured how related models not exactly solvable should behave in the…

We introduce a new wave formulation for the relativistic Euler equations with vacuum boundary conditions that consists of a system of non-linear wave equations in divergence form with a combination of acoustic and Dirichlet boundary…

This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…

When the parameters of electron - extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crutially important…