| 新的变系数可积耦合非线性Schr(o)dinger方程及其孤子解 |
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| 引用本文： | 王灯山,陈静.新的变系数可积耦合非线性Schr(o)dinger方程及其孤子解[J].数学年刊A辑(中文版),2012,33(2):149-160. |
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| 作者姓名： | 王灯山 陈静 |
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| 作者单位： | 北京信息科技大学理学院;中央财经大学应用数学学院 |
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| 基金项目： | 国家自然科学基金(No.11001263,No.11126244);北京市教育委员会科技发展计划基金(No.KM201110772017)资助的项目 |
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| 摘 要： | 基于延拓结构和Hirota双线性方法研究了广义的变系数耦合非线性Schrdinger方程.首先导出了3组新的变系数可积耦合非线性Schrdinger方程及其线性谱问题(Lax对),然后利用Hirota双线性方法给出了它们的单、双向量孤子解.这些向量孤子解在光孤子通讯中有重要的应用.
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| 关 键 词： | 延拓结构 Lax对 Hirota方法 向量孤子 耦合非线性Schrdinger方程 |
New Integrable Variable-Coefficient Coupled Nonlinear Schr(o)dinger Equations and Their Soliton Solutions |
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| WANG Dengshan and CHEN Jing.New Integrable Variable-Coefficient Coupled Nonlinear Schr(o)dinger Equations and Their Soliton Solutions[J].Chinese Annals of Mathematics,2012,33(2):149-160. |
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| Authors: | WANG Dengshan and CHEN Jing |
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| Institution: | 1 School of Science,Beijing Information Science and Technology University,Beijing 100192,China. 2 School of Applied Mathematics,Central University of Finance and Economics, Beijing 100081,China. |
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| Abstract: | A generalized variable-coefficient coupled nonlinear Schrodinger equation is studied by the prolongation structure and the Hirota’s method.Three new integrable variable-coefficient coupled nonlinear Schrodinger equations and their linear spectral problems(Lax pairs) are derived.Then the one- and two-vector soliton solutions to these integrable equations are obtained by means of Hirota’s method.These vector solutions may have important applications in the optical soliton communications. |
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| Keywords: | Prolongation structure Lax pair Hirota’s method Vector solitons Coupled nonlinear Schrdinger equation |
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