This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schrödinger equations (NLS) system with variable coefficients. Indeed, we show, employing similarity transformations, 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. A Mathematica file has been prepared as supplementary material, verifying the Riccati systems used in the construction of the solutions.
ESCORCIA, JOSÉ M., and Erwin Suazo. "ON EXPLICIT SOLITON SOLUTIONS AND BLOW-UP FOR COUPLED VARIABLE COEFFICIENT NONLINEAR SCHRODINGER EQUATIONS." arXiv preprint arXiv:2310.14440 (2023).