In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlevé property. We then solve the LSRI equation using Painlevé truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide ...

Our concern in this talk is the problem of free surface water waves, the form of solitary wave solutions, and their behavior under collisions. Solitary waves for the Euler equations have been described since the time of Stokes. In a long wave perturbation regime they are well described by single soliton solutions of the Korteweg deVries equation (KdV). It is a famous result that multiple solito...

The   ) ( exp    -expansion method is a promising method for finding exact traveling wave solutions to nonlinear evolution equations in physical sciences. In this article, we use the   ) ( exp    -expansion method to find the exact solutions for the nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation and the good Boussinesq equations. Many solitary wave solutions are formally d...

Considered herein is the stability problem of solitary wave solutions of a generalized Ostrovsky equation, which is a modification of the Korteweg-de Vries equation widely used to describe the effect of rotation on surface and internal solitary waves or capillary waves.

We consider the existence and propagation of nondi ractive and nondispersive spatiotemporal optical wavepackets in nonlinear Kerr media. We report analytically and con rm numerically the properties of spatiotemporal dark line solitary wave solutions of the (2+1)D nonlinear Schrödinger equation (NLSE). Dark lines represent holes of light on a continuous wave background. Moreover, we consider non...

We prove that the Cauchy problem for a certain sixth order hyperelastic dispersive equation is globally well-posed in a natural space. We also show that there exist solitary wave solutions u(x, y, t) = φc(x − ct, y) that come from an associated variational problem. Such solitary waves are nonlinearly stable in the sense that if a solution is initially close to the set of such solitary waves, it...

A nonlinear numerical model of long-lived Jovian vortices has been constructed. We assume that the measured zonal velocity profile i(y) extends into the adiabatic interior, but that the eddies and large oval structures are confined to a shallow stably stratified upper layer. Each vortex is stationary with respect to the shear flow & ( y ) at a critical latitude y , that is close to the latitude...

There has been a large amount of work aimed at understanding the stability of nonlinear dispersive equations that support solitary wave solutions[20, 7, 3, 6, 19, 29, 28, 30, 35, 36]. Much of this work relies on understanding detailed properties of the spectrum of the operator obtained by linearizing the flow around the solitary wave. These spectral properties, in turn, have important implicati...

In their recent manuscript Lei Zhao et al. claim that they have constructed an algorithm for automatic construction of solitary wave solutions to nonlinear partial differential equations based on the Exp-function method. We argue that this algorithm does inherit all problems associated to the Exp-function method. We show that this algorithm produces solutions which do not satisfy the original d...

We study the shape of solitary wave pulses that propagate in an infinite chain of beads initially in contact with no compression. For this system, the repulsive force between two adjacent beads is proportional to the pth power of the distance of approach of their centers with p = 3 2 . It is known that solitary wave solutions exist for such a system when p > 1. We prove extremely fast, double-e...