Group-invariant solutions of a nonlinear acoustics model
J. C. Ndogmo
TL;DR
This paper classifies symmetry reductions of a nonlinear acoustics equation, deriving all similarity solutions and analyzing their properties to enhance understanding of the equation's invariant solutions.
Contribution
It provides a complete classification of similarity reductions and group-invariant solutions for the Zabolotskaya-Khokhlov equation based on symmetry analysis.
Findings
All similarity reductions into ODEs are obtained.
Large classes of group-invariant solutions are identified.
Properties of reduced equations and solutions are discussed.
Abstract
Based on a recent classification of subalgebras of the symmetry algebra of the Zabolotskaya-Khokhlov equation, all similarity reductions of this equation into ordinary differential equations are obtained. Large classes of group-invariant solutions of the equation are also determined, and some properties of the reduced equations and exact solutions are discussed.
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