Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
Year: 2025
Type: article
Abstract: This research provides study about the cubic-quartic nonlinear Schrödinger equation (CQNLSE), a basic mathematical model with applications in nonlinear optics , plasma physics , and Bose-Einstein condensates. Accurate solutions to such equations are important to understand the behavior of nonlinear waves , including formation of dark solitons . Traditional numerical methods contain discretization and linearization errors, which limits their accuracy and efficiency. To overcome such challenges, a novel hybrid semi-analytical method is proposed in this study, named as Sumudu-HPM, which combines the Sumudu transform with the homotopy perturbation method (HPM). The Sumudu transform simplifies tackling of initial conditions and converts governing equation into an algebraic form, while HPM generates a recursive approximation to the solution. This hybrid approach preserves the nonlinearity of the system without discretization or linearization. The fetched semi-analytical dark soliton solutions claim excellent agreement with exact solutions across a wide range of time levels, demonstrating accuracy, efficiency, and robustness of proposed method. The key novelty of this work is in the application of Sumudu-HPM approach to solve cubic-quartic nonlinear Schrödinger equation, which bridges the gap between transform-based techniques and perturbation methods for complex nonlinear wave models. The proposed method provides a computationally efficient, stable, and accurate prototype to tackle highly nonlinear partial differential equations , which makes it a valuable tool for researchers across nonlinear science, engineering, and applied mathematics. The main novelty of this work is to develop and implement an efficient semi-analytical technique which is free from discretization error and is computationally efficient.
Source: Results in Optics
Author: Mamta Kapoor
Institution: Marwadi University
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,470
OpenAlex ID: W4411277548