New multi-order envelope periodic solutions to the cubic nonlinear Schrodinger equation

Abstract

Abstract:

Based on the Lame equation and Lame functions, the perturbation method and Jacobi elliptic function expansion method are applied to construct the multi-order exact solutions to the cubic nonlinear Schrodinger equation. Some new multi-order envelope periodic solutions are found among the nonlinear evolution equation. These multi-order envelope periodic solutions correspond to different periodic solutions, which can degenerate into the different envelope solitary solutions. It is shown that some multi-order asymptotic periodic solutions to some nonlinear evolution equations in term of Jacobi elliptic functions and Lame equation are explicitly obtained with the aid of symbolic computation.

Key words: nonlinear equation, multi-order envelope periodic solutions, perturbation method, Lame equation, Jacobi elliptic function, cubic nonlinear Schrodinger equation

CLC Number:

O175.2

XIAO Ya-feng, XUE Hai-li, ZHANG Hong-qing. New multi-order envelope periodic solutions to the cubic nonlinear Schrodinger equation[J]. J4, 2012, 29(3): 269-278.

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