耦合Schrödinger-Boussinesq方程组的显式精确解

广西师范大学学报（自然科学版） ›› 2013, Vol. 31 ›› Issue (1): 11-15.

耦合Schrödinger-Boussinesq方程组的显式精确解

周建军^1,2, 洪宝剑^1,2, 卢殿臣¹

1.江苏大学理学院,江苏镇江212013;
2.南京工程学院基础部,江苏南京211167

收稿日期:2012-06-10 出版日期:2013-03-20 发布日期:2018-11-26
通讯作者: 洪宝剑(1977—),男,江西九江人,江苏大学博士研究生。E-mail:hongbaojian@163.com
基金资助:
国家自然科学基金资助项目(61070231);南京工程学院重点科研基金资助项目(KXJA2010011)

New Jacobi Elliptic Functions Solutions of the Schrödinger-Boussinesq Equations

ZHOU Jian-jun^1,2, HONG Bao-jian^1,2, LU Dian-chen¹

1.Faculty of Science,Jiangsu University,Zhenjiang Jiangsu 212013,China;
2.Department of Basic Courses,Nanjing Institute of Technology,Nanjing Jiangsu 211167,China

Received:2012-06-10 Online:2013-03-20 Published:2018-11-26

摘要/Abstract

摘要： 耦合Schrödinger-Boussinesq方程组广泛应用于激光物理、等离子体物理等领域的一些具体物理过程,如Langmuir场的振幅、电磁波强度以及调幅的不稳定性等,本文通过推广的Jacobi椭圆函数展开法,借助Mathematica软件,求出了耦合Schrödinger-Boussinesq方程组一系列新的Jaocobi椭圆函数复合形式的精确解,部分解在极限情况下退化为孤立波解和三角函数解,丰富、简化和发展了已有的结果。

关键词: 耦合Schrodinger-Boussinesq方程组, 推广的Jacobi椭圆函数展开法, Jacobi椭圆函数解, 精确解

Abstract: Generalized Schrödinger-Boussinesq equations are widely used in the physical fields to describe various physical processes in Laser and plasma,such as Langmuir field amplitude and intense electromagnetic waves and modulational instabilities,etc.In this paper,by using the extended Jacobi elliptic founctions expansion methods,and with the aid of mathematical software,a series of new compound Jacobi formal exact solutions of the Schrödinger-Boussinesq equations are obtained.Some of which weredegenerated to the solitary wave solutions and the single triangle function solutions extreme cases.Thus this method can replenish,simplify and develop the known results.

Key words: Schrodinger-Boussinesq equations, extended Jacobi elliptic functions expansion method, Jacobi elliptic functions solutions, exact solution

中图分类号:

O175.29

周建军, 洪宝剑, 卢殿臣. 耦合Schrödinger-Boussinesq方程组的显式精确解[J]. 广西师范大学学报（自然科学版）, 2013, 31(1): 11-15.

ZHOU Jian-jun, HONG Bao-jian, LU Dian-chen. New Jacobi Elliptic Functions Solutions of the Schrödinger-Boussinesq Equations[J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(1): 11-15.

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