Exploring Wave Function Dynamics in Quantum Mechanics with Nonlinear Interaction

Abstract

The nonlinear Schrödinger-Bopp-Podolsky system has recently attracted a lot of interest since it is useful for modelling a variety of physical phenomena, including optical solitons and Bose-Einstein condensates. In this article, we used an enhanced modified extended tanh-expansion approach to examine the dynamics of wave functions in quantum mechanics with nonlinear interactions and relativistic effects on the Schrödinger-Bopp-Podolsky system. The proposed approach provides precise and effective analytical results. In order to develop a generalized version of the solitary wave solution ansatz, we first formulate the Schrödinger-Bopp-Podolsky system as a coupled set of nonlinear partial differential equations. The enhanced approach enables us to efficiently explore a large parameter space and locate numerous families of solitary wave solutions that have distinctive characteristics. In order to examine the characteristics of solitary waves of the Schrödinger-Bopp-Podolsky system under various conditions, such as variation in the nonlinearity coefficients and external potentials, we employ our enhanced approach. The results of this investigation considerably advance knowledge of the Schrödinger-Bopp-Podolsky system and its solitary wave behavior. The distinctive feature of this article is, to give graphical representations of the obtained solutions using MATLAB and Mathematica simultaneously. Future research into related nonlinear wave equations and their applications in other physical systems will benefit greatly from the enhanced approach described here. © 2026 NSP