Wave Solutions Of Nonlinear Evolution Equations Research Articles

New Periodic Wave Solutions to Generalized Klein–Gordon and BenjaminEquations

By making use of extended mapping method and auxiliary equationfor finding new periodic wave solutions of nonlinear evolutionequations in mathematical physics, we obtain some new periodic wavesolutions for generalized Klein–Gordon equation and Benjamin equation,which cannot be found in previous work. This method also can be usedto find new periodic wave solutions of other nonlinear evolutionequations.

A New Generalized Riccati Equation Rational Expansion Method to GeneralizedBurgers–Fisher Equation with Nonlinear Terms of Any Order

In this paper, based on a new more generalansätz, a new algebraic method, named generalized Riccatiequation rational expansion method, is devised forconstructing travelling wave solutions for nonlinear evolutionequations with nonlinear terms of any order. Compared with mostexisting tanh methods for finding travelling wave solutions, theproposed method not only recovers the results by most known algebraicmethods, but also provides new and more general solutions. We choosethe generalized Burgers–Fisher equation with nonlinear terms of anyorder to illustrate our method. As a result, we obtain several newkinds of exact solutions for the equation. This approach can also beapplied to other nonlinear evolution equations with nonlinear termsof any order.

Abundant New Exact Solutions of the Coupled Potential KdV Equation and the Modified KdV-Type Equation

Abstract Exact solutions of nonlinear evolution equations (NLEEs)in soliton theory and their applications are studied. A powerful method is established to search for exact travelling wave solutions of NLEEs. We chose the coupled potential KdV equation and modified KdV-type equations presented by Foursov to illustrate the approach with the aid of Maple. As a result, eight families of exact solutions of the coupled potential KdV equation and nine families of exact solutions of the modified KdV-type equations are obtained, which contain new kink-like soliton solutions, kink­ shaped solitons, bell-shaped solitons, periodic solutions, rational solutions and singular solitons. The properties of the solutions are shown in figures.