Lie Symmetries, Solitary Waves, and Noether Conservation Laws for (2+1)-Dimensional Anisotropic Power-Law Nonlinear Wave Systems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Lie Symmetries, Solitary Waves, and Noether Conservation Laws for (2+1)-Dimensional Anisotropic Power-Law Nonlinear Wave Systems

Popis výsledku v původním jazyce

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&apos;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.

Název v anglickém jazyce

Lie Symmetries, Solitary Waves, and Noether Conservation Laws for (2+1)-Dimensional Anisotropic Power-Law Nonlinear Wave Systems

Popis výsledku anglicky

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&apos;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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Symmetry

ISSN

2073-8994

e-ISSN

2073-8994

Svazek periodika

17

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

38

Strana od-do

1445

Kód UT WoS článku

001581069500001

EID výsledku v databázi Scopus

2-s2.0-105017275617