[1]陈冬冬,刘玉清.混合正、负阶KdV-mKdV方程精确解[J].常州大学学报(自然科学版),2015,(04):113-115.[doi:10.3969/j.issn.2095-0411.2015.04.021]
　CHEN Dongdong,LIU Yuqing.Exact Solutions to A Mixed Positive-Negative KdV-mKdV Equation[J].Journal of Changzhou University(Natural Science Edition),2015,(04):113-115.[doi:10.3969/j.issn.2095-0411.2015.04.021]
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混合正、负阶KdV-mKdV方程精确解()
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常州大学学报(自然科学版)[ISSN:2095-0411/CN:32-1822/N]

卷:
期数:
2015年04期
页码:
113-115
栏目:
数理科学
出版日期:
2015-11-15

文章信息/Info

Title:
Exact Solutions to A Mixed Positive-Negative KdV-mKdV Equation
作者:
陈冬冬; 刘玉清
常州大学 数理学院,江苏 常州213164
Author(s):
CHEN Dongdong; LIU Yuqing
School of Mathematics and Physics, Changzhou University, Changzhou 213164,China
关键词:
混合正、负阶KdV-mKdV方程;  行波约化;  精确解;  孤子解;  三角函数解
Keywords:
mixed positive-negative KdV-mKdV equation;  reduction of traveling wave method;  exact solutions;  soliton solutions;  triangle function solutions
分类号:
O 175.23
DOI:
10.3969/j.issn.2095-0411.2015.04.021
文献标志码:
A
摘要:
负阶KdV方程与著名的Camassa-Holm方程以及一些高维非线性发展方程有着紧密的联系,同时负阶KdV方程本身往往还具有一些特殊性质比如具有显式弱解。因此负阶方程具有重要的数学和物理价值。本文提出混合正、负阶KdV-mKdV方程,是对负阶KdV方程的一种推广,该方程有许多性质有待研究。通过行波约化,求得方程的精确解是其中一个重要部分。得到了孤子解,三角函数解等形式的解,了解了正、负阶方程共同作用的方式。
Abstract:
Negative KdV equation closely relates to celebrated Camassa-Holm equation and some high dimensional nonlinear evolution equations. In the mean time negative KdV equation itself possess special properties such as explicit weak solution. So negative equations have significant mathematical and physical values. A mixed positive-negative KdV-mKdV equation is proposed in this paper, which is a generalization of negative KdV equation, for which there are several aspects to be researched. Finding its exact solutions through the reduction of traveling wave method is an important part. Some exact solutions such as soliton solutions and triangle function solutions are obtained and the combined action model of positive and negative equations is found then.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2015-01-18。作者简介:陈冬冬(1992—),男,江苏连云港人。指导教师:刘玉清(1966—),男,副教授,E-mail:yqmaiL321@163.com
更新日期/Last Update: 2015-10-20