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

José M. Escorcia and Erwin Suazo ()
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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

Mathematics, 2024, vol. 12, issue 17, 1-21

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.

Keywords: coupled nonlinear Schrödinger equations; soliton solution; rogue wave solution; blow-up solution; similarity transformations; Riccati systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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