Reductions and exact solutions of a cubic Schrodinger Partial Differential Equation

TL;DR

This paper uses Lie symmetry analysis and the double reduction theorem to find exact solutions and conservation laws for a cubic Schrödinger PDE, advancing methods for solving complex differential equations.

Contribution

It applies Lie symmetry analysis and the generalized double reduction theorem to derive exact solutions and conservation laws for a cubic Schrödinger PDE.

Findings

Constructed Noether symmetries and conservation laws.

Derived exact solutions for the cubic Schrödinger PDE.

Enhanced analytical methods for complex PDEs.

Abstract

Lie symmetry analysis is an established method for generating symmetries of differential equations. We apply this method together the generalized fundamental theorem of double reduction. In particular, Noether symmetries and some associated conservation laws are constructed in our investigation to find exact solutions of higher order partial differential equations and complex partial differential equations.