| 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,2012,33(2):149~160 |
| 新的变系数可积耦合非线性Schr(o)dinger方程及其孤子解 |
| New Integrable Variable-Coefficient Coupled Nonlinear Schr(o)dinger Equations and Their Soliton Solutions |
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| DOI： |
| 中文关键词: 延拓结构 Lax对 Hirota方法 向量孤子 耦合非线性Schr(o)dinger方程 |
| 英文关键词:Prolongation structure, Lax pair, Hirota’s method, Vector solitons,
Coupled nonlinear Schr¨odinger equation |
| 基金项目:国家自然科学基金，北京市教育委员会科技发展计划基金 |
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| 中文摘要: |
| 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Schr(o)dinger方程.首先导出了3组新的变系数可积耦合非线性Schr(o)dinger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. |
| 英文摘要: |
| A generalized variable-coefficient coupled nonlinear Schr¨odinger equation is studied
by the prolongation structure and the Hirota’s method. Three new integrable variablecoefficient
coupled nonlinear Schr¨odinger 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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