A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

作者：Yomba Emmanuel^*

来源：Physics Letters, Section A: General, Atomic and Solid State Physics , 2008, 372(7): 1048-1060.

DOI：10.1016/j.physleta.2007.09.003

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First. we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l, n, p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l, n, p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions.

• 出版日期2008-2-11