数学系“60周年”系庆系列报告 一个一般的向量(n+m)元非线性薛定谔方程



活动地点:腾讯 会议

活动时间:2020-07-22 15:00:00

报告主题:一个一般的向量(n+m)元非线性薛定谔方程

报告人:耿献国 教授 (郑州大学)

报告时间:2020年7月22日(周三) 15:00-17:00

参会方式:腾讯 会议

https://meeting.tencent.com/s/0s24mPGE78ga

会议ID:930 508 427

主办部门:理学院数学系

报告摘要:A vector general nonlinear Schr?dinger equation with (m+n) components is proposed, which is a new integrable generalization of the vector nonlinear Schr?dinger equation and the vector derivative nonlinear Schr?dinger equation. Resorting to the Riccati equations associated with the Lax pair and the gauge transformations between the Lax pairs, a general N-fold Darboux transformation of the vector general nonlinear Schr?dinger equation with (m+n) components is constructed, which can be reduced directly to the classical N-fold Darboux transformation and the generalized Darboux transformation without taking limits. As an illustrative example, some exact solutions of the two-component general nonlinear Schr?dinger equation are obtained by using the general Darboux transformation, including a first-order rogue-wave solution, a fourth-order rogue-wave solution, a breather solution, a breather–rogue-wave interaction, two solitons and the fission of a breather into two solitons.

 

 

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