修正的w/g-展开法与非线性Klein-Gordon系统新的行波解

A modified w/g-expansion method and new travelling wave solutions for nonlinear Klein-Gordon systems

目的寻找一个新的构造非线性发展方程解的展开法,以获得更多的非线性发展方程的行波解。方法对现有的w/g-展开法进行改进,并利用改进后的w/g-展开法构造了带有五次非线性项的一般化Klein-Gordon方程与耦合的非线性Klein-Gordon方程组的行波解。结果与结论借助新辅助方程的已知解与符号计算软件Maple17,得到了非线性Klein-Gordon系统新的指数函数解、双曲函数解与三角函数解等精确解。

Purposes—To find out a new expansion method of constructing a nonlinear evolution equation so as to obtain more travelling wave solutions for nonlinear evolution equations.Methods—The existing w/g-expansion method is modified and the travelling wave solutions of the generalized Klein-Gordon equation with quintic nonlinearity and the coupled nonlinear Klein-Gordon equations is constructed with the new modified method.Results and conclusions—Abundant new exact solutions,which include exponential function solutions,hyperbolic function solutions,and triangular function solutions etc.,are discovered with the help of the known solutions satisfying an auxiliary equation and symbolic computation software Maple17.