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广义带导数的非线性Schrödinger方程的动态分析和精确解

杨娜 陈龙伟 熊梅

杨娜, 陈龙伟, 熊梅. 广义带导数的非线性Schrödinger方程的动态分析和精确解[J]. 应用数学和力学, 2018, 39(10): 1198-1205. doi: 10.21656/1000-0887.380302
引用本文: 杨娜, 陈龙伟, 熊梅. 广义带导数的非线性Schrödinger方程的动态分析和精确解[J]. 应用数学和力学, 2018, 39(10): 1198-1205. doi: 10.21656/1000-0887.380302
YANG Na, CHEN Longwei, XIONG Mei. Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1198-1205. doi: 10.21656/1000-0887.380302
Citation: YANG Na, CHEN Longwei, XIONG Mei. Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1198-1205. doi: 10.21656/1000-0887.380302

广义带导数的非线性Schrödinger方程的动态分析和精确解

doi: 10.21656/1000-0887.380302
基金项目: 国家自然科学基金(11761075)
详细信息
    作者简介:

    杨娜(1991—),女,硕士(E-mail: 513327775@qq.com);陈龙伟(1967—),男,博士(通讯作者. E-mail: tc715@sina.com).

  • 中图分类号: O357.41

Dynamic Analysis and Exact Solution of the General Nonlinear Schrödinger Equation With Derivative

Funds: The National Natural Science Foundation of China(11761075)
  • 摘要: 利用动力系统方法,针对广义带导数的非线性Schrödinger方程的精确解问题进行研究分析.采用行波变换,将其化为常微分方程动力系统;计算出该方程动力系统的首次积分,讨论了系统在不同参数条件下的奇点与相图,得到对应的精确解,包括孤立波解、周期波解、扭结波解和反扭结波解.运用数值模拟的方法,对方程的光滑孤立波解和周期波解等进行了数值模拟。分析计算获得的结果完善了相关文献已有的研究成果.
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出版历程
  • 收稿日期:  2017-12-05
  • 修回日期:  2018-01-17
  • 刊出日期:  2018-10-01

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