具有Kuramoto-Sivashinsky扰动的广义Zakharov-Kuznetsov方程孤立波解的存在性  

Existence of solitary wave solutions of generalized Zakharov-Kuznetsov equation with Kuramoto-Sivashinsky perturbation

作　　者：温倩 郑航 WEN Qian;ZHENG Hang(College of Mathematics and Computer,Wuyi University,Wuyishan 354300,China)

机构地区：[1]武夷学院数学与计算机学院,福建武夷山354300

出　　处：《延边大学学报（自然科学版）》2023年第2期102-108,共7页Journal of Yanbian University（Natural Science Edition）

基　　金：福建省中青年教师教育科研项目(JAT200670,JAT210454)。

摘　　要：利用几何奇异摄动理论研究了一个具有Kuramoto-Sivashinsky(KS)扰动的广义Zakharov-Kuznetsov(GZK)方程孤立波解的存在性.首先,利用动力系统分支理论计算了扰动GZK方程对应的未扰系统同宿轨道的显式表达式;其次,在扰动参数充分小的情况下利用Melnikov积分计算并得到了KS扰动下的GZK方程存在孤立波解的充分条件;最后,用数值方法证明了所得结果的正确性.Based on geometric singular perturbation,the existence of solitary wave solutions of a generalized Zakharov-Kuznetsov(GZK)equation with Kuramoto-Sivashinsky(KS)perturbation was studied.Firstly,the exact parametric expression of homoclinic orbit for unperturbed system was given by method of the bifurcation theory of dynamic system.Secondly,when the perturbed parameter was sufficiently small,the sufficient conditions to guarantee the existence of solitary wave solutions of the GZK equation with KS perturbation was obtained via the Melnikov function integral.Finally,the correctness of the obtained results was proved by numerical method.

关 键 词：几何奇异摄动理论 Melnikov积分 广义Zakharov-Kuznetsov方程 同宿轨道 孤立波解 

分 类 号：O193[理学—数学]