Soliton solutions, sensitivity analysis, and multistability analysis for the modified complex Ginzburg-Landau model

Abstract This study mainly focuses on finding new soliton solutions for a modified complex Ginzburg-Landau equation. This model describes the wave profile shown in different physical systems. To begin with, we apply an analytical algorithm, namely the extended modified auxiliary equation mapping method to investigate the complex wave structures for abundant solutions related to the modified complex Ginzburg-Landau model. Complex wave structures have a wider range of solutions, stemming from nonlinear models, featuring more intricate dynamics, necessitating advanced modeling techniques, and posing greater challenges in validation and optimization compared to traditional wave solutions. The complex wave conversion is considered to make a differential equation. Various types of solutions to the underlying equation, including solutions trigonometric, hyperbolic, and exponential, have been realized in the study. Secondly, the planer system is extracted from the given equation. Later, the considered equation’s sensitivity is examined using sensitivity analysis. The multistability analysis is also presented at the end after including a perturbed term. Numerical simulations are included with the analytical results to improve understanding of the solutions’ dynamic behavior. Our newly obtained solutions profoundly impact the improvement of new theories of fluid dynamics, mathematical physics, soliton dynamics, optical physics, quantum mechanics, and some other physical and natural sciences. To the best of our knowledge, this is the first time that the methods we present are used for the equation we consider. All obtained solutions are verified for validity using the Maple software program.