Dullin-Gottwald-Holm方程尖峰孤立子附近解的稳定性  

Orbital stability of solutions near the peakons for Dullin-Gottwald-Holm equation

作　　者：丁丹平[1] 韩希凤 DING Dan-ping;HAN Xi-feng(School of Mathematical Sciences,Jiangsu University,Zhenjiang 212013,Jiangsu,China)

机构地区：[1]江苏大学数学科学学院,江苏镇江212013

出　　处：《西北师范大学学报（自然科学版）》2021年第6期18-24,共7页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11371175)。

摘　　要：研究Dullin-Gottwald-Holm(DGH)方程Cauchy问题在尖峰孤立子附近的解的轨道稳定性.运用伪共形变换方法,对DGH方程Cauchy问题在尖峰孤立波附近的解做如下分解:λ^(1/2)(t)u(t,y+x(t))=ε(t,y)+Q(y).通过对控制参数λ(t),x(t)的讨论,证明了余项ε(t,y)的稳定性;进一步得到了DGH方程Cauchy问题尖峰孤立波及其附近解的轨道稳定性.结果表明:若初值0与u 0在H 1意义下充分接近,则在时间T内初值对应的解仍任意接近,即(t,·+r 2)-u(t,·+r 1)H^(1)<ω,t∈[0,T).The orbital stability of solutions around the peakons for Cauchy problem of the Dullin-Gottwald-Holm(DGH)equation is studied in this paper.Applying the method of pseudo-conformal transformation,the solution of DGH equation near the peakon is decomposed into following form:λ^(1/2)(t)u(t,y+x(t))=ε(t,y)+Q(y).By discussing the modulation parametersλ(t)and x(t),the stability of residual termε(t,y)is proved.Furthermore,the orbital stability of peakon solutions and near the peakons of Cauchy problem for DGH equation are obtained.The stability theorem indicates that,if the initial data 0 is sufficiently close to u 0 in H 1,then two corresponding solutions remain close within time T,that is(t,·+r 2)-u(t,·+r 1)H^(1)<ω,t∈[0,T).

关 键 词：Dullin-Gottwald-Holm(DGH)方程 尖峰孤立波解 轨道稳定性 伪共形变换 

分 类 号：O175.29[理学—数学]