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Hirota Bilinear Approach to Multi-Component Nonlocal Nonlinear Schrödinger Equations

Author

Listed:
  • Yu-Shan Bai

    (Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China)

  • Li-Na Zheng

    (Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China)

  • Wen-Xiu Ma

    (Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
    Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA
    School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, South Africa)

  • Yin-Shan Yun

    (Department of Mathematics, Inner Mongolia University of Technology, Hohhot 010051, China)

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.

Suggested Citation

  • Yu-Shan Bai & Li-Na Zheng & Wen-Xiu Ma & Yin-Shan Yun, 2024. "Hirota Bilinear Approach to Multi-Component Nonlocal Nonlinear Schrödinger Equations," Mathematics, MDPI, vol. 12(16), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2594-:d:1461708
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    References listed on IDEAS

    as
    1. Deng, Xiao & Lou, Senyue & Zhang, Da-jun, 2018. "Bilinearisation-reduction approach to the nonlocal discrete nonlinear Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 477-483.
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