广义Zakharov-Kuznetsov方程的新精确解

New exact solutions of generalized Zakharov-Kuznetsov equation

应用扩展到负次幂的(G′/G^(2))展开法对广义Zakharov-Kuznetsov方程进行求解.在不同条件下得到广义Zakharov-Kuznetsov方程的9组新精确解,包含双曲函数解、三角函数解和有理函数解.对精确解中的参数赋值,利用符号计算软件Maple给出部分解的数值模拟图,并对怪波现象产生的原因进行分析.扩展的(G′/G^(2))展开法有计算简单、直接的特点,可以应用于其它非线性偏微分方程的求解研究中.

The generalized Zakharov-Kuznetsov equation is solved by using the(G′/G^(2))expansion method extended to negative power.Under different conditions,nine new exact solutions of the generalized Zakharov-Kuznetsov equation are obtained,including hyperbolic function solutions,trigonometric function solutions and rational function solutions.For the parameter assignment in the exact solution,the numerical simulation diagram of the partial solution is given by using the symbolic calculation software Maple,and the causes of the rogue wave phenomenon are analyzed.The extended(G′/G^(2))expansion method has the characteristics of simple and direct calculation,and can be applied to the solution of other nonlinear partial differential equations.