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组合KdV方程的双扭结孤立波及其稳定性研究
  • 期刊名称：物理学报
  • 时间：2011.2.2
  • 页码：020402-
  • 分类：O411.1[理学—理论物理;理学—物理]
  • 作者机构：[1]西北师范大学物理与电子工程学院,兰州730070
  • 相关基金：国家自然科学基金（批准号：10575082 11047010）; 教育部科学技术研究重点项目（批准号：209128）; 西北师范大学科技创新工程（批准号：NWNU-KJCXGC-03-53）资助的课题~~
  • 相关项目：磁流体中的非线性波及其稳定性研究
作者： 石玉仁|张娟|杨红娟|段文山|
关键词： cKdV方程, 双扭结单孤子, 稳定性, cKdV equation, single soliton solution with double kinks, stability
中文摘要：

利用扩展的双曲函数法得到了combined KdV-mKdV（cKdV）方程的几类精确解,其中一类为具有扭结-反扭结状结构的双扭结单孤子解.在不同的极限情况下,该解分别退化为cKdV方程的扭结状或钟状孤波解.理论分析表明,cKdV方程既有传播型孤立波解,也有非传播型孤立波解.文中对双扭结型孤立波解的稳定性进行了数值研究,结果表明,cKdV方程既存在稳定的双扭结型孤立波,也存在不稳定的双扭结型孤立波.

英文摘要：

Based on the ideas of the hyperbola function expansion method,we obtained some analytical solutions of the combined KdV-mKdV （cKdV） equations by introducing new expansion functions. One of the single soliton solutions has the kink-antikink structure,and this solution reduces to the kink-like solution and the bell-like solution under different limitations. Theoretical analysis shows that the cKdV equation has both propagated-type and non-propagated-type solitary wave solutions. We also investigated the stability of the single solitary wave solution with double kinks numerically. The results indicate that the solution may be stable or unstable,depending on different sets of parameters.

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