Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach
The present study is devoted to obtaining some exact generalized solutions and new solitary wave solutions for a (2+1)-dimensional nonlinear rth dispersionless Dym (rdDym) equation by utilizing the Lie symmetry analysis. The Lie infinitesimals, geometric vector fields, the commutation relation of th...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-05-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379721003478 |
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| author | Sachin Kumar Hassan Almusawa Amit Kumar |
| author_facet | Sachin Kumar Hassan Almusawa Amit Kumar |
| author_sort | Sachin Kumar |
| collection | DOAJ |
| description | The present study is devoted to obtaining some exact generalized solutions and new solitary wave solutions for a (2+1)-dimensional nonlinear rth dispersionless Dym (rdDym) equation by utilizing the Lie symmetry analysis. The Lie infinitesimals, geometric vector fields, the commutation relation of the symmetry Lie algebra are derived by employing the Lie group symmetry technique. Thenceforth, explicit exact closed-form solutions are achieved through two stages of symmetry reductions. These closed-form solutions include arbitrary independent functional parameters and other constant parameters, therefore exhibiting rich localized solitons and comprising the existing solutions in the literature. Furthermore, the different dynamical wave structures of established soliton solutions in the forms of oscillating periodic multisolitons, the interaction between four lump-solitons with parabolic waves, W-shaped solitons, and the interaction between two-doubly solitons with parabolic waves, periodic multi-solitons, and parabolic-shaped solitons profiles are exhibited graphically through three-dimensional plots. |
| first_indexed | 2024-12-16T13:18:56Z |
| format | Article |
| id | doaj.art-caa6cdc42414429fa96d69d0248b56b7 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-16T13:18:56Z |
| publishDate | 2021-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-caa6cdc42414429fa96d69d0248b56b72022-12-21T22:30:24ZengElsevierResults in Physics2211-37972021-05-0124104201Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approachSachin Kumar0Hassan Almusawa1Amit Kumar2Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India; Corresponding author.Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Mathematics, Sri Venkateswara College, University of Delhi, Delhi 110021, IndiaThe present study is devoted to obtaining some exact generalized solutions and new solitary wave solutions for a (2+1)-dimensional nonlinear rth dispersionless Dym (rdDym) equation by utilizing the Lie symmetry analysis. The Lie infinitesimals, geometric vector fields, the commutation relation of the symmetry Lie algebra are derived by employing the Lie group symmetry technique. Thenceforth, explicit exact closed-form solutions are achieved through two stages of symmetry reductions. These closed-form solutions include arbitrary independent functional parameters and other constant parameters, therefore exhibiting rich localized solitons and comprising the existing solutions in the literature. Furthermore, the different dynamical wave structures of established soliton solutions in the forms of oscillating periodic multisolitons, the interaction between four lump-solitons with parabolic waves, W-shaped solitons, and the interaction between two-doubly solitons with parabolic waves, periodic multi-solitons, and parabolic-shaped solitons profiles are exhibited graphically through three-dimensional plots.http://www.sciencedirect.com/science/article/pii/S2211379721003478(2+1)-dimensional rdDym equationLie symmetry techniqueSymmetry reductionsExact closed-form solutionsSolitons |
| spellingShingle | Sachin Kumar Hassan Almusawa Amit Kumar Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach Results in Physics (2+1)-dimensional rdDym equation Lie symmetry technique Symmetry reductions Exact closed-form solutions Solitons |
| title | Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach |
| title_full | Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach |
| title_fullStr | Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach |
| title_full_unstemmed | Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach |
| title_short | Some more closed-form invariant solutions and dynamical behavior of multiple solitons for the (2+1)-dimensional rdDym equation using the Lie symmetry approach |
| title_sort | some more closed form invariant solutions and dynamical behavior of multiple solitons for the 2 1 dimensional rddym equation using the lie symmetry approach |
| topic | (2+1)-dimensional rdDym equation Lie symmetry technique Symmetry reductions Exact closed-form solutions Solitons |
| url | http://www.sciencedirect.com/science/article/pii/S2211379721003478 |
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