ON KINK AND ANTI-KINK WAVE SOLUTIONS OF SCHR&#214;DINGER EQUATION WITH DISTRIBUTED DELAY

Chuanhai Xu; Yuhai Wu; Lixin Tian; Boling Guo

doi:10.11948/2018.1385

2018 Volume 8 Issue 5

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Chuanhai Xu, Yuhai Wu, Lixin Tian, Boling Guo. ON KINK AND ANTI-KINK WAVE SOLUTIONS OF SCHRÖDINGER EQUATION WITH DISTRIBUTED DELAY[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1385-1395. doi: 10.11948/2018.1385

Citation:

Chuanhai Xu, Yuhai Wu, Lixin Tian, Boling Guo. ON KINK AND ANTI-KINK WAVE SOLUTIONS OF SCHRÖDINGER EQUATION WITH DISTRIBUTED DELAY[J]. Journal of Applied Analysis & Computation, 2018, 8(5): 1385-1395. doi: 10.11948/2018.1385

ON KINK AND ANTI-KINK WAVE SOLUTIONS OF SCHRÖDINGER EQUATION WITH DISTRIBUTED DELAY

1 Nonlinear Science Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China;
2 School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu 210023, China;
3 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

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Abstract

Abstract

This paper deals with existence problem of traveling wave solutions of a class of nonlinear Schrödinger equation having distributed delay with a strong generic kernal. By using the geometric singular perturbation theory and the Melnikov function method, we establish results of the existence of kink and anti-kink wave solutions of the nonlinear Schrödinger equation with time delay when the average delay is sufficiently small.
- Nonlinear Schrödinger equation /
- kink and anti-kink wave solutions /
- geometric singular perturbation theory /
- Melnikov function /
- distributed delay
MSC: 34D15;35B25

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