Classification of Multiply Travelling Wave Solutions for Coupled Burgers, Combined KdV-Modified KdV, and Schrödinger-KdV Equations

Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

Nonlinear Stability of Solitary Travelling-wave Solutions for the Kawahara-kdv and Modified Kawahara-kdv Equations

In this paper we establish the nonlinear stability of solitary travelling-wave solutions for the Kawahara-KdV equation ut + uux + uxxx − γ1uxxxxx = 0, and the modified Kawahara-KdV equation ut + 3u 2ux + uxxx − γ2uxxxxx = 0, where γi ∈ R is a positive number when i = 1, 2. The main approach used to determine the stability of solitary travelling-waves will be the theory developed by Albert in [1].

Travelling Wave Solutions for the Painlevé-integrable Coupled Kdv Equations

We study the travelling wave solutions for a system of coupled KdV equations derived by Lou et al [11]. In that paper, they found 5 types of Painlevé integrable systems for the coupled KdV system. We show that each of them can be reduced to a partially or completely uncoupled system, through which the dynamical behavior of travelling wave solutions can be determined. In some parameter regions, ...

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...

Complex-Valued Burgers and KdV-Burgers Equations

Spatially periodic complex-valued solutions of the Burgers and KdV-Burgers equations are studied in this paper. It is shown that for any sufficiently large time T , there exists an explicit initial data such that its corresponding solution of the Burgers equation blows up at T . In addition, the global convergence and regularity of series solutions is established for initial data satisfying mil...