基于辅助函数法的耦合Shrodinger-KdV方程的函数解研究

Research on functional solutions of coupled Shrodinger-KdV equations based on auxiliary function method

利用辅助函数法,得到耦合Shrodinger-KdV方程在参数β>-1/2的条件下的一些Jacobi椭圆函数解.根据椭圆函数的性质,将部分椭圆函数解退化为三角函数解和双曲函数解,利用Mathematica对部分波形图模拟,并分析波形图显示空间周期性和爆破性的特点.结果表明,基于辅助函数法得到耦合Shr?dinger-KdV方程的27组解,其中有15组椭圆函数解、7组三角函数解和5组双曲函数解,它们具有对称性和空间周期性及爆破性的特点.

By using the auxiliary function method,some Jacobi elliptic function solutions for the coupled Shrodinger-KdV equation are obtained under the condition of parameter β-1/2.Based on the properties of elliptic functions,partial elliptic function solutions are reduced to trigonometric and hyperbolic function solutions.Mathematica is used to simulate partial waveform diagrams and analyze the characteristics of spatial periodicity and blowup in waveform diagrams.The results show that based on the auxiliary function method,27 sets of solutions for the coupled Shrodinger-KdV equation are obtained,including 15 sets of elliptic function solutions,7 sets of trigonometric function solutions,and 5 sets of hyperbolic function solutions,which have the characteristics of symmetry,spatial periodicity,and blowup.