Dynamics investigation of (1+1)-dimensional time-fractional potential Korteweg-de Vries equation
| Autor: | Nageela Anum, Ghazala Akram, Maria Sarfraz, Maasoomah Sadaf |
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| Rok vydání: | 2022 |
| Předmět: |
Residual power series method
Power series Work (thermodynamics) Wave solutions Caputo fractional derivative Dynamics (mechanics) One-dimensional space General Engineering Characteristic equation Engineering (General). Civil engineering (General) Residual Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Applied mathematics Jumarie’s modified Riemann-Liouville derivative TA1-2040 Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Modified auxiliary equation method Mathematics |
| Zdroj: | Alexandria Engineering Journal, Vol 61, Iss 1, Pp 501-509 (2022) |
| ISSN: | 1110-0168 |
| DOI: | 10.1016/j.aej.2021.06.023 |
| Popis: | The potential Korteweg-de Vries equation arises in the study of water waves and is reported in the dynamics of tsunami waves. The fractional order potential Korteweg-de Vries equation is more flexible and generalized than its classical form. In this work, the modified auxiliary equation technique and residual power series method are utilized to build new exact and analytical approximate solutions of the time-fractional potential Korteweg-de Vries equation. The dynamics of the solutions obtained are explored by drawing them in two and three dimensions. Comparisons between the new results and the solutions available in literature show that the presented approaches of nonlinear problem resolution are highly effective and reliable. The obtained solutions will be helpful to understand the dynamical framework of many nonlinear physical phenomena. |
| Databáze: | OpenAIRE |
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