(2+1)维色散长波方程组新的无穷序列精确解

New infinite sequence exact solutions of a set of (2+1)-dimensional dispersive wave equations

为了获得非线性发展方程的无穷序列新精确解,给出了Riccati方程的一些新解和Bcklund变换以及解的非线性叠加公式。Riccati方程与函数变换相结合,借助符号计算系统Mathematica,构造了(2+1)维色散长波方程组新的无穷序列精确解。这些解包括无穷序列类孤子解、无穷序列复合型解等。这种方法在构造非线性发展方程无穷序列精确解领域具有普遍意义。

To seek new infinite sequence exact solutions for nonlinear evolution equations, the formula of nonlinear superposition of some new solutions and Backlund transformation of Riccati equation are given, and combining Riccati equation with function transformation, new infinite sequence exact solutions to a set of （2＋1）-dimensional dispersive wave equations are constructed with the aid of symbolic computation system Mathematica, which includes infinite sequence soliton-like solutions and infinite sequence complex solutions. The method is of significance to seek infinite sequence exact solutions to other nonlinear evolution equations.