摘要
为了得到广义KdV-mKd方程新的精确解形式,应用扩展的G′/G展开方法,结合新的辅助方程,根据齐次平衡理论,进行KdV-mKdV方程精确解和相应怪波形成机理的研究,并得到广义KdV-mKdV方程新的精确解,这些解主要由双曲函数、三角函数和有理函数组成,其中还包含mKdV方程的部分解形式。根据解的待定形式中待定参数之间的关系,通过应用Maple软件画图和对解的详细分析,解释了不同条件下相应怪波形成的机理。所得结果对理解自然界中的怪波现象具有启发作用。
In order to obtain some new exact solutions of the general KdV-mKdV equation,combining with the new auxiliary ordinary equations and the homogeneous balance theory,improvedG′/Gmethod was proposed and was applied to study new solutions and theory of rogue wave.The solutions were constructed by hyperbolic,trigonometric and rational function forms for the general KdV-mKdV equation,which included a part of solutions of mKdV equation in particular.According to the relationship between these parameters in the undetermined form of the solution,the formation mechanism of the corresponding rogue waves was explained by the graph of the new solutions in detail.It was important to explain the rogue waves phenomenon in nature.
作者
郭春晓
郭艳凤
GUO Chunxiao;GUO Yanfeng(Department of Mathematics,China University of Mining and Technology(Beijing),Beijing100083,China;School of Science,Guangxi University of Science and Technology,Liuzhou545006,Guangxi,China;School of Mathematics and Physics,China University of Geosciences,Wuhan430074,Hubei,China)
出处
《河南理工大学学报（自然科学版）》
CAS
北大核心
2021年第5期175-180,共6页
Journal of Henan Polytechnic University（Natural Science）
基金
国家自然科学基金资助项目(11861013,11771444)
中国矿业大学(北京)越崎青年学者基金资助项目
广西自然科学基金资助项目(2017GXNSFAA198221)
中国地质大学(武汉)中央高校科研项目(2018061)。
