Lie Symmetries, Solitary Waves, and Noether Conservation Laws for (2+1)-Dimensional Anisotropic Power-Law Nonlinear Wave Systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258506" target="_blank" >RIV/61989100:27740/25:10258506 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2073-8994/17/9/1445" target="_blank" >https://www.mdpi.com/2073-8994/17/9/1445</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym17091445" target="_blank" >10.3390/sym17091445</a>
Alternative languages
Result language
angličtina
Original language name
Lie Symmetries, Solitary Waves, and Noether Conservation Laws for (2+1)-Dimensional Anisotropic Power-Law Nonlinear Wave Systems
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics
Result continuities
Project
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Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Symmetry
ISSN
2073-8994
e-ISSN
2073-8994
Volume of the periodical
17
Issue of the periodical within the volume
9
Country of publishing house
CH - SWITZERLAND
Number of pages
38
Pages from-to
1445
UT code for WoS article
001581069500001
EID of the result in the Scopus database
2-s2.0-105017275617