散焦mKdV方程的N重暗孤子解的行列式表示

Abstract

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

CLC Number:

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

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