一类具有波动算子非线性Schrdinger方程的新多级包络周期解  

New multi-stage envelope periodic solutions for a class of nonlinear Schrdinger equation with wave operator

作　　者：林成龙[1] 梁宗旗[1] 杜瑞连[1] LIN Cheng-long, LIANG Zong-qi, DU Rui-lian(College of Science, Jimei University, Xiamen 361021, Chin)

机构地区：[1]集美大学理学院, 福建厦门361021

出　　处：《高校应用数学学报（A辑）》2018年第2期211-222,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：福建省科技厅重点项目(2014H0034); 福建省高校产学研科技项目(2017H6015); 福建省自然科学基金(2016J01310; 2017J01402; JZ160450)

摘　　要：该文给出了求解具有波动算子的非线性Schrdinger方程包络周期解的一种新方法.首先在构建的微分动力系统中分析了其平衡解的特性,其次通过将Lam方程及新的Lam函数与Jacobi椭圆函数展开法进行结合的办法得到了新的多级包络周期解,最后在极限条件下获得该方程相应的新包络孤波解以及其他形式的解.A new method for solving nonlinear Schrodinger equation with wave operator is proposed. Fristly, the characteristics of the equilibrium solution of the transformed dierential equation are analyzed in the dierential dynamical system. Secondly, the envelope periodic solutions in di？erent forms are obtained by combining Lam？e equation, a new Lame function and Jacobi elliptic function expansion method. Finally, under extreme conditions, new solitary wave solutions and other forms of solutions are presented.

关 键 词：非线性SCHRODINGER方程 波动算子 Lame函数 JACOBI椭圆函数 平衡解 多级包络周期解 

分 类 号：O241.8[理学—计算数学]