New Soliton Solutions of Time-Fractional Korteweg–de Vries Systems

Model construction for different physical situations, and developing their solutions, are the major characteristics of the scientific work in physics and engineering. Korteweg–de Vries (KdV) models are very important due to their ability to capture different physical situations such as thin film flo...

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Bibliographic Details
Published in:Universe (Basel) 2022-08, Vol.8 (9), p.444
Main Authors: Qayyum, Mubashir, Ahmad, Efaza, Riaz, Muhammad Bilal, Awrejcewicz, Jan, Saeed, Syed Tauseef
Format: Article
Language:English
Subjects:
Algorithms
Deformation
dispersive long-wave KdV system
fractional-order system
generalized Hirota–Satsuma KdV system
homotopy perturbation method
Homotopy theory
Korteweg–de Vries system
Laplace transform
Laplace transformation
Laplace transforms
Lie groups
Partial differential equations
Physics
Quantum field theory
Shallow water
Solitons
Thin films
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Summary:Model construction for different physical situations, and developing their solutions, are the major characteristics of the scientific work in physics and engineering. Korteweg–de Vries (KdV) models are very important due to their ability to capture different physical situations such as thin film flows and waves on shallow water surfaces. In this work, a new approach for predicting and analyzing nonlinear time-fractional coupled KdV systems is proposed based on Laplace transform and homotopy perturbation along with Caputo fractional derivatives. This algorithm provides a convergent series solution by applying simple steps through symbolic computations. The efficiency of the proposed algorithm is tested against different nonlinear time-fractional KdV systems, including dispersive long wave and generalized Hirota–Satsuma KdV systems. For validity purposes, the obtained results are compared with the existing solutions from the literature. The convergence of the proposed algorithm over the entire fractional domain is confirmed by finding solutions and errors at various values of fractional parameters. Numerical simulations clearly reassert the supremacy and capability of the proposed technique in terms of accuracy and fewer computations as compared to other available schemes. Analysis reveals that the projected scheme is reliable and hence can be utilized with other kernels in more advanced systems in physics and engineering.
ISSN:2218-1997
2218-1997
DOI:10.3390/universe8090444