（2+1）维改进的Zakharov-Kuznetsov方程的无穷序列复合型类孤子新解∗

摘要

对(G′/G)展开法做了进一步的研究，利用两次函数变换将二阶非线性辅助方程的求解问题转化为一元二次代数方程与Riccati方程的求解问题。借助Riccati方程的Bäcklund变换及解的非线性叠加公式获得了辅助方程的无穷序列解。这样，利用(G′/G)展开法可以获得非线性发展方程的无穷序列解，这一方法是对已有方法的扩展，与已有方法相比可获得更丰富的无穷序列解。以(2+1)维改进的Zakharov-Kuznetsov方程为例得到了它的无穷序列新精确解。这一方法可以用来构造其他非线性发展方程的无穷序列解。%The (G′/G)-expansion method is further studied, the solution to the second-order nonlinear auxiliary equation is changed into solving of one unknown quadratic equation and Riccati equation by two function transformations. An infinite sequence solution of auxiliary equation is obtained with the help of Bäcklund transformation of Riccati equation and nonlinear superposition formula of the solution. In this way, the infinite sequence solution to the nonlinear evolution equation can be obtained by the (G′/G)-expansion method, this method is an extension of existing methods, which can get more infinite series solutions. Take the (2+1)-dimensional Zakharov-Kuznetsov modified equal width equation as an example to obtain the new infinite sequence solution. This method can be used to get the infinite sequence solution to other nonlinear evolution equations.