应用Bernoulli型简单方程求(2+1)维KP方程的精确行波解

Application of Simplest Equations to Bernoulli Kind for Obtaining Exact Traveling-Wave Solutions for the (2 + 1)-Dimensional KP Equation

利用行波变换把(2+1)维KP方程化成常微分方程,再运用简单方程法求解(2+1)维KP方程的行波解.文中选取Bernoulli方程为简单方程.将由KP方程所化成的常微分方程分成两部分:一部分包含导数项,另一部分为方程其他部分.然后,平衡最高次幂的非线性项所产生的最高次数和最高阶导数项所产生的最高项的次数,得到平衡方程,确定解的形式.最后解得(2+1)维KP方程的行波解.

Traveling-wave coordinate is used for transforming KP equation to a nonlinear ordinary differential equation .The traveling-wave solutions of KP equation are obtained by the method of the simplest equation when the simplest equation is the Bernoulli equation .The nonlinear ordinary equation is divided into two parts：part A con-tains the derivatives, and part B contains the rest of the equation .Then,balancing the highest powers of the polyno-mials for the parts A and B and a balance equation is obtained which depends on the kind of the simplest equation , the form of solution is determined .Finally, the new traveling-wave solutions of the KP equation are obtained .