Meromorphic Solutions of Modified Quintic Complex Ginzburg-Landau Equation

TL;DR

This paper derives explicit meromorphic solutions for the modified quintic complex Ginzburg-Landau equation, including periodic and rational solutions, using a Laurent series-based algorithm, advancing analytical methods for nonlinear differential equations.

Contribution

The paper introduces a novel application of Demina and Kudryashov's algorithm to find explicit meromorphic solutions of the modified quintic complex Ginzburg-Landau equation.

Findings

Derived general explicit solutions in three forms

Identified simply periodic, doubly periodic, and rational solutions

Validated solutions through a specific case study

Abstract

In this paper, the meromorphic solution of the modified quintic complex Ginzburg-Landau equation (CGLE) is analysed. We found the general explicit solutions to the equation in three different forms, yield simply periodic, doubly periodic and rational solution. Firstly, this equation was transformed to nonlinear ordinary differential equation and then we solved it by using a powerful algorithm proposed by Demina and Kudryashov, based on the existence of Laurent series. Finally, we have the meromorphic solution of the equation, and to verify these solutions, we showed a special case which we constructed from the general form.