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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2018, Vol. 33 Issue (2): 211-222    DOI:
    
New multi-stage envelope periodic solutions for a class of nonlinear Schrodinger equation with wave operator
LIN Cheng-long, LIANG Zong-qi, DU Rui-lian
College of Science, Jimei University, Xiamen 361021, China
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Abstract  A new method for solving nonlinear Schr?odinger equation with wave operator is
proposed. Fristly, the characteristics of the equilibrium solution of the transformed di?erential equation
are analyzed in the differential dynamical system. Secondly, the envelope periodic solutions in different
forms are obtained by combining Lame 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.

Key words： nonlinear Schrodinger equation      wave operator      Lame function      Jacobi elliptic function       equilibrium solution      multi-order envelope periodic solutions      
Published: 26 July 2018
CLC:  O241.8  
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LIN Cheng-long
LIANG Zong-qi
DU Rui-lian
Cite this article:

LIN Cheng-long, LIANG Zong-qi, DU Rui-lian. New multi-stage envelope periodic solutions for a class of nonlinear Schrodinger equation with wave operator. Applied Mathematics A Journal of Chinese Universities, 2018, 33(2): 211-222.

URL:

http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2018/V33/I2/211


一类具有波动算子非线性Schrodinger方程的新多级包络周期解

该文给出了求解具有波动算子的非线性Schr?odinger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Lame方程
及新的Lame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.

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 
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