The nondegenerate solitons solutions for the vcGCNLS equations with four-wave mixing terms via the Hirota bilinear method

Abstract In this article, we delve into the variable coefficient generalized coupled nonlinear Schrödinger (vcGCNLS) equations with four-wave mixing terms in the context of a birefringent fiber, encompassing time-dependent diffraction, nonlinearity, and gain (loss) parameters. Utilizing the Hirota bilinear method, we derive the bilinear forms of the equations. Subsequently, we calculate the nondegenerate one-soliton and two-solitons solutions. Thereafter, by adjusting the complex wave parameters, we analyze the dynamic behaviors of solitons. Additionally, through varying the diffraction parameter and nonlinear coefficient, we successfully obtain nondegenerate double-hump solitons of diverse shapes.