Group-invariant solutions of a nonlinear acoustics model

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.

14 pages

References in corpus (1)

• Integrable systems without the Painlevé property

Cited by in corpus (1)

• Analysis of the symmetry group and exact solutions of the dispersionless KP equation in $n+1$ dimensions