Kinetic equation for nonlinear wave-particle interaction: Solution properties and asymptotic dynamics

Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation

Three Long Wave Asymptotic Regimes for the Nonlinear-schrödinger Equation

We survey some recent results related to three long wave asymptotic regimes for the Nonlinear-Schrödinger Equation: the Euler regime corresponding to the WKB method, the linear wave regime and finally the KdV/KP-I asymptotic dynamics.

Travelling Wave Solution of Two-Dimensional Nonlinear KdV-Burgers Equation

Abstract In this study, we present two different methods a sech-tanh method and extended tanh-method to obtained the soliton solutions of the two-dimensional Korteweg-de Vries-Burgers (KdVB) equation with the initial conditions. These solutions include bright and dark solitary wave solutions, triangular solutions and complex line soliton wave solution. These solutions are stable and have applic...

Global Strong Solution to a Nonlinear Dispersive Wave Equation

In this paper, compared with the previous results, a new global existence for strong solutions to the equation is acquired provided that the potential (1−∂2 x)u0 changes sign on R, which improves considerably the previous result. Mathematics Subject Classification: 35G25, 35L05, 35Q35

Global Existence, Uniqueness, and Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation