散焦mKdV方程的N重暗孤子解的行列式表示

数学物理学报 ›› 2016, Vol. 36 ›› Issue (1): 14-26.

散焦mKdV方程的N重暗孤子解的行列式表示

虞静¹, 韩敬伟², 王立洪³, 贺劲松³

1 杭州电子科技大学理学院杭州 310018;
2 杭州电子科技大学信息工程学院杭州 310018;
3 宁波大学理学院浙江宁波 315211

收稿日期:2015-07-09 修回日期:2015-12-26 出版日期:2016-02-25 发布日期:2016-02-25
作者简介:贺劲松,hejingsong@nbu.edu.cn,jshe@ustc.edu.cn
基金资助:
国家自然科学基金(11271210,61273077);浙江省自然科学基金(LQ12A01002)和浙江省高等学校访问学者专业发展项目(FX2012013)资助

Determinant Representation of Dark N-Soliton Solution for the Defocusing Modified Korteweg-de Vries Equation

Yu Jing¹, Han Jingwei², Wang Lihong³, He Jingsong³

1 School of Science, Hangzhou Dianzi University, Hangzhou 310018;
2 School of Information Engineering, Hangzhou Dianzi University, Hangzhou 310018;
3 School of Science, Ningbo University, Zhejiang Ningbo 315211

Received:2015-07-09 Revised:2015-12-26 Online:2016-02-25 Published:2016-02-25
Supported by:
Supported by the NSFC (11271210, 61273077), the Zhejiang Provincial Natural Science Foundation of China (LQ12A01002) and the Professional Development Program of Zhejiang Province College Visiting Scholar (FX2012013)

摘要/Abstract

摘要：

该文首先构造了耦合的mKdV方程的新的达布变换,同时显式给出了它的达布矩阵T_N和新解q^[N],r^[N]的行列式表示.其次,考虑将约化条件r=q^*附加到该达布变换上,以及考虑一个周期的非零种子解,得到了散焦mKdV方程的N重暗孤子解的行列式表示.最后,证明了暗的单孤子解和暗的2孤子解是光滑的,进一步证明了暗的N(N≥2)孤子解至少在某一邻域内是光滑的.

关键词: 达布变换, 行列式表示, 散焦mKdV方程

Abstract:

For coupled modified Korteweg-de Vries (mKdV) equation, we construct a new Darboux transformation (DT), whose Darboux matrix T_N and transformed solutions q^[N], r^[N] are explicitly given in determinant form. When the reduction condition r=q^* is imposed on the new DT and a periodic non-zero seed solution is considered, we obtain determinant representation of dark N-soliton solutions for the defocusing mKdV equation. Especially, we show that dark 1-soliton and dark 2-soliton are both smooth solutions, and furthermore, we show that dark N-soliton solutions are smooth at least on a certain domain.

Key words: Darboux transformation, Determinant representation, Defocusing mKdV equation

中图分类号:

虞静, 韩敬伟, 王立洪, 贺劲松. 散焦mKdV方程的N重暗孤子解的行列式表示[J]. 数学物理学报, 2016, 36(1): 14-26.

Yu Jing, Han Jingwei, Wang Lihong, He Jingsong. Determinant Representation of Dark N-Soliton Solution for the Defocusing Modified Korteweg-de Vries Equation[J]. Acta mathematica scientia,Series A, 2016, 36(1): 14-26.

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