On exact solutions of nonlinear acoustic equations

TL;DR

This paper derives exact solutions for nonlinear acoustic equations that model strong sound pulse propagation with curved wave fronts in multiple dimensions, providing a basis for solving more complex related equations.

Contribution

It introduces a simple physical approach to obtain exact solutions and proposes an ansatz applicable to a broader class of Khokhlov-Zabolotskaya type equations.

Findings

Solutions describe focused and defocused sound pulses in different transverse directions

Method simplifies solving complex nonlinear acoustic equations

Potential for extending solutions to more general wave propagation problems

Abstract

Solutions of nonlinear acoustic equations describing propagation of strong sound pulses with account of curvature of wave fronts in multi-dimensional geometry are obtained from simple physical considerations. The form of these solutions suggests ansatz suitable for finding solutions of much more general equations of Khokhlov-Zabolotskaya type. General method is illustrated by an example of nonlinear sound pulse focused in one transverse direction and defocused in the other direction.