WEN Qian,ZHENG Hang.Existence of solitary wave solutions of generalized Zakharov-Kuznetsov equation with Kuramoto-Sivashinsky perturbation[J].Journal of Yanbian University,2023,(02):102-108.
具有Kuramoto-Sivashinsky扰动的广义Zakharov-Kuznetsov方程孤立波解的存在性
- Title:
- Existence of solitary wave solutions of generalized Zakharov-Kuznetsov equation with Kuramoto-Sivashinsky perturbation
- 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
- Keywords:
- geometric singular perturbation; Melnikov integral; generalized Zakharov-Kuznetsov equation; homoclinic orbit; solitary wave solution
- 分类号:
- O193
- 文献标志码:
- A
- 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.
- Abstract:
- 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.
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备注/Memo
收稿日期: 2023 03 23
基金项目: 福建省中青年教师教育科研项目(JAT200670,JAT210454)
作者简介: 温倩(1981—),女,硕士,讲师,研究方向为微分方程.