Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM

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 wa...

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Main Author: Mamta Kapoor
Format: Article
Language:English
Published: Elsevier 2025-12-01
Series:Results in Optics
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Online Access:http://www.sciencedirect.com/science/article/pii/S2666950125000859
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author Mamta Kapoor
author_facet Mamta Kapoor
author_sort Mamta Kapoor
collection DOAJ
description 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.
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spelling doaj-art-7285cbcbc6154fe6b673c1405687c8312025-08-20T02:07:34ZengElsevierResults in Optics2666-95012025-12-012110085710.1016/j.rio.2025.100857Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPMMamta Kapoor0Marwadi University Research Center, Department of Mathematics, Faculty of Engineering & Technology, Marwadi University, Rajkot 360003 Gujarat, IndiaThis 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.http://www.sciencedirect.com/science/article/pii/S2666950125000859Sumudu transformHomotopy perturbation methodCubic-Quartic non-linear Schrödinger equation
spellingShingle Mamta Kapoor
Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
Results in Optics
Sumudu transform
Homotopy perturbation method
Cubic-Quartic non-linear Schrödinger equation
title Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
title_full Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
title_fullStr Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
title_full_unstemmed Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
title_short Dark soliton solutions of cubic-quartic non-linear Schrödinger equation via Sumudu HPM
title_sort dark soliton solutions of cubic quartic non linear schrodinger equation via sumudu hpm
topic Sumudu transform
Homotopy perturbation method
Cubic-Quartic non-linear Schrödinger equation
url http://www.sciencedirect.com/science/article/pii/S2666950125000859
work_keys_str_mv AT mamtakapoor darksolitonsolutionsofcubicquarticnonlinearschrodingerequationviasumuduhpm