Hirota Bilinear Approach to Multi-Component Nonlocal Nonlinear Schrödinger Equations-Reference-Cited by-同舟云学术

Hirota Bilinear Approach to Multi-Component Nonlocal Nonlinear Schrödinger Equations

Published:2024-08-22 Issue:16 Volume:12 Page:2594
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Bai Yu-Shan¹^ORCID,Zheng Li-Na¹,Ma Wen-Xiu²³⁴⁵^ORCID,Yun Yin-Shan¹

Affiliation:

1. Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China

2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

3. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA

5. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa

Abstract

Nonlocal nonlinear Schrödinger equations are among the important models of nonlocal integrable systems. This paper aims to present a general formula for arbitrary-order breather solutions to multi-component nonlocal nonlinear Schrödinger equations by using the Hirota bilinear method. In particular, abundant wave solutions of two- and three-component nonlocal nonlinear Schrödinger equations, including periodic and mixed-wave solutions, are obtained by taking appropriate values for the involved parameters in the general solution formula. Moreover, diverse wave structures of the resulting breather and periodic wave solutions with different parameters are discussed in detail.

Funder

Natural Science Foundation of Inner Mongolia

National Natural Science Foundation of China

Fundamental research funds for the universities directly under the Inner Mongolia Autonomous Region

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/16/2594/pdf

Reference27 articles.

1. Fibich, G. (2015). The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse, Springer International Publishing.

2. Breather solutions to the focusing nonlinear Schrödinger equation;Tajiri;Phys. Rev. E,1998

3. Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media;Zakharov;J. Exp. Theor. Phys.,1971

4. Inverse scattering transformation for generalized nonlinear Schrödinger equation;Zhang;Appl. Math. Lett.,2019

5. Gu, C., Hu, H., and Zhou, X. (2005). Darboux Transformations in Integrable Systems, Springer.