Resonant NLSE in the presence of spatio-temporal and intermodal dispersion is dominated by a myriad of nonlinearities

Abstract This article is dedicated to investigating a myriad of nonlinear forms of the resonant nonlinear Schrödinger equation, which is one of the essential examples of evolution equations, and providing some observations. The resonant nonlinear Schrödinger equation, in the presence of spatio-temporal and inter-modal dispersion, was addressed using the recently introduced Kudryashov’s method, and solution functions were obtained for eleven different nonlinear forms (Kerr, power, parabolic, dual-power, polynomial, triple-power, quadratic-cubic, generalized quadratic-cubic, anti-cubic, generalized anti-cubic, and parabolic law with non-local nonlinearity). The study will contribute to the literature not only by examining such a diverse set of nonlinear forms together but also by investigating the impact of the degree of nonlinearity and the coefficients of different nonlinearity terms on soliton behavior. Detailed examinations of all these points, the results obtained, observations, and necessary comments have been made in the relevant sections.