Lie Symmetries, Solitary Waves, and Noether Conservation Laws for (2 + 1)-Dimensional Anisotropic Power-Law Nonlinear Wave Systems
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| Publicado en: | Symmetry vol. 17, no. 9 (2025), p. 1445-1483 |
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| Otros Autores: | , , |
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MDPI AG
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 022 | |a 2073-8994 | ||
| 024 | 7 | |a 10.3390/sym17091445 |2 doi | |
| 035 | |a 3254649367 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 231635 |2 nlm | ||
| 100 | 1 | |a Samina, Samina |u General Education Centre, Quanzhou University of Information Engineering, Quanzhou 362000, China; samina@qzuie.edu.cn | |
| 245 | 1 | |a Lie Symmetries, Solitary Waves, and Noether Conservation Laws for (2 + 1)-Dimensional Anisotropic Power-Law Nonlinear Wave Systems | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This study presents the complete analysis of a (2 + 1)-dimensional nonlinear wave-type partial differential equation with anisotropic power-law nonlinearities and a general power-law source term, which arises in physical domains such as fluid dynamics, nonlinear acoustics, and wave propagation in elastic media, yet their symmetry properties and exact solution structures remain largely unexplored for arbitrary nonlinearity exponents. To fill this gap, a complete Lie symmetry classification of the equation is performed for arbitrary values of m and n, providing all admissible symmetry generators. These generators are then employed to systematically reduce the PDE to ordinary differential equations, enabling the construction of exact analytical solutions. Traveling wave and soliton solutions are derived using Jacobi elliptic function and sine-cosine methods, revealing rich nonlinear dynamics and wave patterns under anisotropic conditions. Additionally, conservation laws associated with variational symmetries are obtained via Noether’s theorem, yielding invariant physical quantities such as energy-like integrals. The results extend the existing literature by providing, for the first time, a full symmetry classification for arbitrary m and n, new families of soliton and traveling wave solutions in multidimensional settings, and associated conserved quantities. The findings contribute both computationally and theoretically to the study of nonlinear wave phenomena in multidimensional cases, extending the catalog of exact solutions and conserved dynamics of a broad class of nonlinear partial differential equations. | |
| 653 | |a Behavior | ||
| 653 | |a Conservation laws | ||
| 653 | |a Classification | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Symmetry | ||
| 653 | |a Elliptic functions | ||
| 653 | |a Propagation | ||
| 653 | |a Elastic media | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Power law | ||
| 653 | |a Nonlinear differential equations | ||
| 653 | |a Power | ||
| 653 | |a Traveling waves | ||
| 653 | |a Generators | ||
| 653 | |a Exact solutions | ||
| 653 | |a Wave propagation | ||
| 653 | |a Methods | ||
| 653 | |a Nonlinear systems | ||
| 653 | |a Dynamical systems | ||
| 653 | |a Fluid dynamics | ||
| 653 | |a Acoustics | ||
| 653 | |a Nonlinear dynamics | ||
| 653 | |a Ordinary differential equations | ||
| 653 | |a Solitary waves | ||
| 653 | |a Lie groups | ||
| 653 | |a Nonlinearity | ||
| 700 | 1 | |a Almusawa Hassan |u Department of Mathematics, College of Sciences, Jazan University, Jazan 45142, Saudi Arabia | |
| 700 | 1 | |a Arif Faiza |u Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan; faizaarif71@gmail.com | |
| 700 | 1 | |a Jhangeer Adil |u IT4-Innovations, VSB-Technical University of Ostrava, 70800 Ostrava-Poruba, Czech Republic; adil.jhangeer@vsb.cz | |
| 773 | 0 | |t Symmetry |g vol. 17, no. 9 (2025), p. 1445-1483 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3254649367/abstract/embedded/J7RWLIQ9I3C9JK51?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3254649367/fulltextwithgraphics/embedded/J7RWLIQ9I3C9JK51?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3254649367/fulltextPDF/embedded/J7RWLIQ9I3C9JK51?source=fedsrch |