【摘要】 基于Bell多项式法和试探函数法,研究了一种广义(3+1)维非线性发展方程的Lax可积性及精确解.首先,利用Bell多项式法,获得了广义(3+1)维非线性发展方程的双线性形式、双线性B??cklund变换、Lax对及无穷守恒律.其次,借助该方程的双线性B??cklund变换,给出了对应的解的非线性叠加公式.进一步利用试探函数法,通过解的非线性叠加公式,得到了方程的双孤子解.最后应用Mathematica符号计算系统,通过选取适当的参数,分析了精确解的性质.更多还原

【Abstract】 Based on the Bell polynomial method and the trial function method, we investigate the Lax integrability and exact solutions of a generalized(3+1)-dimensional nonlinear evolution equation.First, by employing the Bell polynomial method, we derive the bilinear form, bilinear B??cklund transformation, Lax pair, and infinite conservation laws of the equation. Second, based on the bilinear B??cklund transformation, we establish the corresponding nonlinear superposition formula for the solutions. Furthermore, using the trial function method, we obtain a double solition solution by solving the nonlinear superposition formula. Finally, with the aid of the Mathematica symbolic computation system, we analyze the properties of the composite solutions by selecting appropriate parameters.更多还原