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On Blow-Up and Explicit Soliton Solutions for Coupled Variable Coefficient Nonlinear Schrödinger Equations

Author

Listed:
  • José M. Escorcia

    (Escuela de Ciencias Aplicadas e Ingeniería, Universidad EAFIT, Carrera 49 No. 7 Sur-50, Medellín 050022, Colombia)

  • Erwin Suazo

    (School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 W. University Drive, Edinburg, TX 78539-2999, USA)

Abstract

This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schrödinger equations (NLS) system with variable coefficients. Indeed, by employing similarity transformations, we show the existence of rogue wave and dark–bright soliton-like solutions for such a generalized NLS system, provided the coefficients satisfy a Riccati system. As a result of the multiparameter solution of the Riccati system, the nonlinear dynamics of the solution can be controlled. Finite-time singular solutions in the L ∞ norm for the generalized coupled NLS system are presented explicitly. Finally, an n-dimensional transformation between a variable coefficient NLS coupled system and a constant coupled system coefficient is presented. Soliton and rogue wave solutions for this high-dimensional system are presented as well.

Suggested Citation

  • José M. Escorcia & Erwin Suazo, 2024. "On Blow-Up and Explicit Soliton Solutions for Coupled Variable Coefficient Nonlinear Schrödinger Equations," Mathematics, MDPI, vol. 12(17), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2694-:d:1467115
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    References listed on IDEAS

    as
    1. Kannan Manikandan & Murugaian Senthilvelan & Roberto André Kraenkel, 2016. "On the characterization of vector rogue waves in two-dimensional two coupled nonlinear Schrödinger equations with distributed coefficients," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(10), pages 1-11, October.
    2. Pereira, Enrique & Suazo, Erwin & Trespalacios, Jessica, 2018. "Riccati–Ermakov systems and explicit solutions for variable coefficient reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 278-296.
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