| Summary: | Finding solutions in the solitary wave-form for nonlinear Schrödinger’s equations with dispersive and dispersion terms is challenging but would yield interesting results. The basic idea of this paper is to use the idea of logarithmic transformation-based approaches in combination with symbolic structures of exponential functions. The article discusses a nonlinear equation that serves as a universal version of Schrödinger’s equations and has numerous applications in the field of nonlinear optics. We obtain a diverse set of solutions involving trigonometric, hyperbolic, and rational forms. These forms have a broad application spectrum in fields such as plasma physics, nonlinear optics, optical fibers, and nonlinear sciences. Due to the presence of various arbitrarily chosen constants, these solutions exhibit extensive and rich dynamical behavior. In this direction, several numerical simulations corresponding to these results are presented in the article. One notable aspect to consider is that the methodologies utilized in this paper have not been previously employed to solve the model being studied. Furthermore, these techniques may be readily adaptable for solving a diverse range of other nonlinear partial differential equations.
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