Generalized Darboux transformation and N-th order rogue wave solution of a general coupled nonlinear Schrödinger equations

Abstract

We construct a generalized Darboux transformation (GDT) of a general coupled nonlinear Schrödinger (GCNLS) system. Using GDT method we derive a recursive formula and present determinant representations for N-th order rogue wave solution of this system. Using these representations we derive first, second and third order rogue wave solutions with certain free parameters. By varying these free parameters we demonstrate the formation of triplet, triangle and hexagonal patterns of rogue waves.

27 pages, 7 figures and Accepted for Publication in Commun. Nonlinear Sci. Numer. Simul

References in corpus (2)

• Capillary rogue waves
• Dark solitons, Breathers and Rogue Wave Solutions of the Coupled Generalized Nonlinear Schrödinger Equations

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• An analysis of spatiotemporal localized solutions in the variable coefficients (3+1)-dimensional nonlinear Schrödinger equation with six different forms of dispersion parameters