ON A CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS (II): AN EXAMPLE OF GCKdV EQUATIONS

Abstract

By using the method of dynamical systems, we continuously study the dynamical behavior for the first class of singular nonlinear traveling wave systems. As an example, the traveling wave solutions for a generalized coupled KdV equations are discussed. Exact explicit parametric representations of solitary wave solutions, periodic wave solutions and kink wave solutions are given.

Peakon, pseudo-peakon, and cuspon solutions for two generalized Camassa-Holm equations

“…Therefore, we know which orbit gives rise to what wave profiles and how the wave profiles are changed depending on the parameters. In addition, applying the first integrals of the integrable traveling wave systems, we are able to get some explicit solutions (see Li et al, 18,19 and Li 11 ).…”

Exact Traveling Wave Solutions and Simulation For A Class Nonlinear Partial Differential Equations

“…There are many methods to be used in travel wave solutions of nonlinear evolution equations, such as the inverse scattering method, the B a  cklund transformation method, algebraic-geometric method, the Darboux transformation method, multiple exp-function method [4] , the Hirota bilinear method [2,3,8] , and dynamical systems method . By applying the dynamical systems method [5,6,7], some new exact solutions of (1.1) are obtained [7] . Since the structure of traveling wave solutions of (1.4) plays a large role in investigating the wave solutions of (1.1), we will study the solutions of traveling wave equations of ( Multiple kink solutions, multiple singular kink solutions and multiple soliton solutions were formally derived [1] and the exact traveling wave solutions of (1.1) have been obtained [7] .To our knowledge the study for the exact traveling wave solutions of (1.4) in different subsets of 4-parameters space of the system (1.7),…”

“…[7] , (1.6) has an exact periodic wave solution (4,5,6)) of (1.6) corresponding to the periodic wave solutions of (1.6) are obtained as follows: …”

Dynamic Behavior of Traveling Wave Solutions for a class of nonlinear partial differential equations

“…In this paper, we research the travel wave solutions of (1.1) by bifucation method of dynamical systems [3,5] . The traveling wave solutions of (1.1) corresponding to peridioc wave solutions and solitary wave solutions, have been found in [5] completely.…”