Bright soliton dynamics for resonant nonlinear Schrödinger equation with generalized cubic–quintic nonlinearity

Abstract For systems modeled by the resonant nonlinear Schrödinger equation (RNLSE) with generalized cubic–quintic nonlinearity, we derive the bright soliton solution of the equation in (1+1) dimensions, using the modified F -expansion method along with the novel ansatz of F -base function. Furthermore, we extend the analytical study of soliton dynamics to higher (2+1) and (3+1) dimensions by using the self-similar method, and demonstrate the soliton behavior via graphical illustration. Moreover, we investigate the effect of the resonance term on bright soliton solution in (1+1) dimensions. Additionally, we consider the nonlinear equation models with perturbation terms and derive the bright soliton solutions for the one-dimensional (1D) to three-dimensional (3D) cases. The theoretical results derived can be used to guide the experimental studies and observations of bright solitons in systems described by RNLSE model.