离散的非线性薛定谔方程的一类精确解

Exact solutions of discrete nonlinear Schrdinger equation

目的研究离散的非线性薛定谔方程的一类精确解。方法利用改进的Jacobi椭圆函数展开法。结果得到包含Jacobi椭圆正弦,Jacobi椭圆余弦,第三类Jacobi椭圆余弦的周期波解并表明在极限情形下得到孤立子解。结论此方法也可以用来求解其他非线性微分-差分方程。

Aim To study exact solutions of discrete nonlinear Schrdinger equation.Methods The study is based on Jacobi elliptic function expansion method.Results Periodic wave solution including Jacobi elliptic sine function,Jacobi elliptic cosine function and the third Jacobi elliptic cosine function are obtained.On the limit condition,the soliton solution can be obtained.Conclusion The method can be also used to solve other nonlinear differential-difference equations.