耦合KdV方程的双峰孤立子及其稳定性  

The single solitary wave with double peaks of the coupled KdV equation and its stability

作　　者：石玉仁[1] 张娟[1] 杨红娟[1] 段文山[1] 

机构地区：[1]西北师范大学物理与电子工程学院,兰州730070

出　　处：《物理学报》2011年第2期56-62,共7页Acta Physica Sinica

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~~

摘　　要：利用扩展双曲函数法求解了耦合KdV方程,得到了6类精确解,其中一类为具有双峰状结构的单孤子解.在不同的极限情况下,该解分别退化为耦合KdV方程的扭结状或钟状孤波解.文中对双峰孤立波的稳定性进行了数值研究,结果表明:耦合KdV方程的双峰孤立波在长波小振幅扰动和小振幅钟型孤立波扰动下,均稳定.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.

关 键 词：cKdV方程 双扭结单孤子 稳定性 

分 类 号：O175.29[理学—数学]