Related papers: Multi-solitons and related solutions for the water…
We prove the existence of asymptotic two-soliton states in the Fermi-Pasta-Ulam model with general interaction potential. That is, we exhibit solutions whose difference in $\ell^2$ from the linear superposition of two solitary waves goes to…
We present a theory for experimentally observed phenomenon of one dimensional asynchronous waves. The general principle of coexistence of linear and nonlinear solutions of a dynamical system is underlying the present theoretical work. The…
We discuss exact multi-soliton solutions to integrable hierarchies on noncommutative space-times in diverse dimension. The solutions are represented by quasi-determinants in compact forms. We study soliton scattering processes in the…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
In this paper, we construct $K$-solitons of the focusing energy-critical nonlinear wave equation in five-dimensional space, i.e. solutions $u$ of the equation such that \begin{equation*}…
It is shown that, under a small perturbation of lump (soliton) for Davey--Stewartson (DS-II) equation, the scattering data gain the nonsoliton structure. As a result, the solution has the form of Fourier type integral. Asymptotic analysis…
It is shown that multisoliton solutions of several well known nonlinear PDEs(x, t) can be obtained by certain separation of variables: each n-soliton arises from a mutual solution of a nonlinear ODE(x), common for all NPDEs considered, and…
Solitary waves in a general nonlinear lattice are discussed, employing as a model the nonlinear Schr\"odinger equation with a spatially periodic nonlinear coefficient. An asymptotic theory is developed for long solitary waves, that span a…
We consider a generalization of the mKdV equation, which contains dissipation terms similar to those contained in both the Benjamin-Bona-Mahoney equation and the famous Camassa-Holm and Degasperis-Procesi equations. Our objective is the…
Breather solutions are considered to be generally accepted models of rogue waves. However, breathers are not localized, while wavefields in nature can generally be considered as localized due to the limited spatial dimensions. Hence, the…
This article provides a naturel sequel of previous works [6, 4] regarding the stability of travelling waves for a general one-dimensional Schr\"odinger equation (N LS) with non-zero condition at infinity. The aim of this article is twofold.…
Considered herein are a number of variants of the Boussinesq type systems modeling surface water waves. Such equations were derived by different authors to describe the two-way propagation of long gravity waves. A question of existence of…
In this work, we study the generalized shallow water wave equation to obtain novel solitary wave solutions. The application of this non-linear model can be found in tidal waves, weather simulations, tsunami prediction, river and irrigation…
We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the…
This work studies the rotation-generalized Benjamin-Ono equation which is derived from the theory of weakly nonlinear long surface and internal waves in deep water under the presence of rotation. It is shown that the solitary-wave solutions…
This study deals with higher-ordered asymptotic equations for the water-waves problem. We considered the higher-order/extended Boussinesq equations over a flat bottom topography in the well-known long wave regime. Providing an existence and…
Propagation of unsteady waves under the effect of a step point load on a square lattice of spring-connected masses is investigated. The problem is solved by two methods. Asymptotic solutions at large time intervals, which describe the…