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| 具有任意阶非线性薛定谔方程的新行波解 | |
| 引用本文： | 王俊杰,王连堂,杨宽德.具有任意阶非线性薛定谔方程的新行波解[J].成都信息工程学院学报,2012,27(1):120-130. |
| 作者姓名： | 王俊杰 王连堂 杨宽德 |
| 作者单位： | 1. 思茅师范高等专科学校,云南普洱665000;西北大学数学系,陕西西安710127 2. 西北大学数学系,陕西西安,710127 3. 思茅师范高等专科学校,云南普洱,665000 |
| 摘 要： | 对具有任意阶非线性薛定谔方程的行波解进行了研究。给出具有任意阶非线性薛定谔方程的精确解。利用行波变换和辅助函数法把具有任意阶非线性薛定谔方程最终转化为一个非线性常微分方程的解,通过对这个微分方程的研究可以得到具有任意阶非线性薛定谔方程的行波解。具有任意阶非线性薛定谔方程存在的孤立波解、三角孤立波解、扭孤立波解、Jacobi椭圆函数解。得到了具有任意阶非线性薛定谔方程新的Jacobi椭圆函数解。 |
| 关 键 词： | 非线性薛定谔方程 Lienard方程 孤波解 扭孤立波 Jacobi椭圆函数 偏微分方程 精确解 |
Some New Exact Traveling Wave Solutions for the Generalized Higher-order Nonlinear Schr(o)dinger Equation with any Order |
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| WANG Jun-jie , WANG Lian-tang , YANG Kuan-de.Some New Exact Traveling Wave Solutions for the Generalized Higher-order Nonlinear Schr(o)dinger Equation with any Order[J].Journal of Chengdu University of Information Technology,2012,27(1):120-130. | |
| Authors: | WANG Jun-jie WANG Lian-tang YANG Kuan-de |
| Institution: | 1(1.Mathematics Department of Simao Teachers College,Pu’er 665000,China;2.Mathematics Department of Northwest University,Xi’an 710127,China) |
| Abstract: | In this paper,traveling wave solutions of the generalized derivative Schrdinger equation with any order are studied.We give exact solutions of the generalized derivative Schrdinger equation with any order.A auxiliary equation expansion method and its algorithm is proposed by studying a second order nonlinear ordinary differential equation.The method is applied to the generalized derivative Schrdinger equation with any order.The generalized derivative Schrdinger equation with any order exist singular solutions,triangular periodic wave solution and Jacobian elliptic function solutions.We give the new Jacobian elliptic function solutions of the generalized derivative Schrdinger equation with any order. |
| Keywords: | nolinear Schrdinger equation Lienard equation solitary wave so-lution triangular periodic wave solution Jacobian elliptic function solutions partialdirerential equation exact solutions |
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