应用改进的G'/G^2展开法求Zakharov方程的精确解

Derivation of exact solutions for Zakharov equation with extended-G′/G^2 expansion method

应用改进的G'/G^2展开法构造出Zakharov方程的18组精确解,这些解主要包括双曲函数通解、三角函数通解和有理函数通解三种形式.当对双曲函数通解中的参数取特殊值时,可以得到孤立波解.对三角函数通解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,应用改进的G'/G^2展开法能够得到Zakharov方程一些新的精确解,扩大了解的范围,这种方法对于研究非线性光学和量子光学具有非常广泛的应用意义。

Using the improved G^1/G^2 expansion method, eighteen groups of exact solutions for Zakharov equation were constructed. As the result, the hyperbolic function solutions, trigonometric function solu- tions, and rational solutions with arbitrary parameters were obtained. When the arbitrary parameters in hyperbolic function solutions were taken as some special values, the solitary wave solutions can be obtained. When the arbitrary parameters in trigonometric function solutions are taken as some special values, the trigonometric function solutions can be expressed as periodic wave solutions. It is proved that application of improved G^1/G^2 expansion method can give some new exact solutions of the Zakharov equation, and increase the scope of the solution. This method has a very wide range of application to fields such as nonlinear optics and quantum optics.