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

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.