Exact Solutions and Classification of the (1+3) Dimensional Generalized Modified Schrödinger Equation Using Symmetry Reduction Approach

Abstract

This study focuses on nonlinear equations, particularly the (1 + 3) dimensional generalized modified Schrödinger equation (GMSE) as a key example. Given the extensive use of classical Lie symmetry methods, the research applies Lie symmetry analysis to explore the (GMSE) in detail. Lie symmetries of the equation are derived to identify rare classes of exact solutions, with the arbitrary functions in each solution offering a wide range of possible solution profiles. The Lie symmetry method holds considerable future potential for generating more diverse solutions, as it allows solutions to incorporate functions and arbitrary constants. This work also effectively highlights the uniqueness of the solutions when compared to previously published results.