构造非线性发展方程无穷序列复合型精确解的一种方法

摘要

为了获得非线性发展方程新的无穷序列复合型精确解,给出了Riccati方程的Backlund变换和解的非线性叠加公式,符号计算系统Mathematica的帮助下,以广义Boussinesq方程为应用实例,获得了无穷序列复合型精确解.这里包括双曲函数、三角函数与有理函数复合解、双曲函数与三角函数复合解等几种新的无穷序列复合型精确解.该方法在构造非线性发展方程无穷序列复合型精确解方面具有普遍意义.%To seek new infinite sequence complexiton solutions to nonlinear evolution equations ( NEE ( s ) ), the formula of nonlinear superposition of the solutions and B(a)cklund transformation of Riccati equation are presented, and as an illusrative exapmle, the generalized Boussinesq equation is chosen to obtain new infinite sequence complexiton solutions with the aid of symbolic computation system Mathematica, which includes complexiton solutions of hyperbolic function, triangular function type with rational function and hyperbolic function with triangular function.The method is of significance to construct infinite sequence complexiton solutions to other NEEs.