Dynamics of three nonisospectral nonlinear Schrödinger equations

doi:10.1088/1674-1056/28/2/020202

中国物理B ›› 2019, Vol. 28 ›› Issue (2): 20202-020202.doi: 10.1088/1674-1056/28/2/020202

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Dynamics of three nonisospectral nonlinear Schrödinger equations

Abdselam Silem, Cheng Zhang(张成), Da-Jun Zhang(张大军)

Department of Mathematics, Shanghai University, Shanghai 200444, China

收稿日期:2018-11-26 修回日期:2018-12-18 出版日期:2019-02-05 发布日期:2019-02-05
通讯作者: Da-Jun Zhang E-mail:djzhang@staff.shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11601312, 11631007, and 11875040).

Dynamics of three nonisospectral nonlinear Schrödinger equations

Abdselam Silem, Cheng Zhang(张成), Da-Jun Zhang(张大军)

Department of Mathematics, Shanghai University, Shanghai 200444, China

Received:2018-11-26 Revised:2018-12-18 Online:2019-02-05 Published:2019-02-05
Contact: Da-Jun Zhang E-mail:djzhang@staff.shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11601312, 11631007, and 11875040).

摘要/Abstract

摘要：

Dynamics of three nonisospectral nonlinear Schrödinger equations (NNLSEs), following different time dependencies of the spectral parameter, are investigated. First, we discuss the gauge transformations between the standard nonlinear Schrödinger equation (NLSE) and its first two nonisospectral counterparts, for which we derive solutions and infinitely many conserved quantities. Then, exact solutions of the three NNLSEs are derived in double Wronskian terms. Moreover, we analyze the dynamics of the solitons in the presence of the nonisospectral effects by demonstrating how the shapes, velocities, and wave energies change in time. In particular, we obtain a rogue wave type of soliton solutions to the third NNLSE.

关键词: nonisospectral nonlinear Schrö, dinger equations, gauge transformations, bilinear forms, solitons, rogue waves

Abstract:

Key words: nonisospectral nonlinear Schrö, dinger equations, gauge transformations, bilinear forms, solitons, rogue waves

中图分类号: (Integrable systems)

02.30.Ik

02.30.Ks (Delay and functional equations) 05.45.Yv (Solitons)

Abdselam Silem, 张成, 张大军. Dynamics of three nonisospectral nonlinear Schrödinger equations[J]. 中国物理B, 2019, 28(2): 20202-020202.

Abdselam Silem, Cheng Zhang(张成), Da-Jun Zhang(张大军). Dynamics of three nonisospectral nonlinear Schrödinger equations[J]. Chin. Phys. B, 2019, 28(2): 20202-020202.

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Dynamics of three nonisospectral nonlinear Schrödinger equations

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