mKdV方程的新型结构孤立波及其动力学不稳定性  

Solitary waves with new structures of mKdV equation and their dynamical instabilities

作　　者：张磊[1] 

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2015年第5期29-32,37,共5页Journal of Northwest Normal University(Natural Science)

基　　金：甘肃省自然科学基金资助项目(1310RJZA076)

摘　　要：在复数范围内讨论了Modified Korteweg de Vries(mKdV)方程孤立波解的结构.发现在一定参数情况下,该解的实部为反向或同向双峰孤立波而虚部为双扭结状孤立波(或反之).接着对文献中提出的有限差分格式进行了理论分析,表明其为二阶精度的条件稳定格式,并解析地给出了数值稳定性条件.最后采用该格式对mKdV方程描述的该类波的动力学稳定性进行了数值研究,发现既存在动力学稳定的孤立波,也存在动力学不稳定的孤立波.The structures of a new type of solitary wave solutions for the mKdV equation within the scope of complex number is discussed . It is found , under certain parameters , that the real part of the solitary solution has two bell‐like peaks with the same direction or inverse direction , while the imaginary part of the solitary wave solution has two kinks . We also made a detailed analysis on the truncation error and the numerical stability for a finite difference scheme presented in relative reference . T he results show that the accuracy of this approach is of order 2 and it is conditional stable . The condition of numerical stable for this scheme is also presented analytically . At last , we numerically investigate the dynamical instability of the solitary waves described by the mKdV equation via the finite difference method . The results indicate that it exists both stable and unstable solitary waves .

关 键 词：MKDV方程 孤立波 有限差分法 动力学不稳定性 

分 类 号：O436.1[机械工程—光学工程]