Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya Equations

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Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a diffraction sound beam in a nonlinear medium. We give a new algebraic method of solving these equations by using certain finite-dimensional stable range of the nonlinear terms and obtain large families of new explicit exact solutions parameterized by several functions for them. These parameter functions enable one to find the solutions of some related practical models and boundary value problems.
21pages; Acta Applicanda Mathematicae, online-first

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Mathematical Physics, Analysis of PDEs, Exactly Solvable and Integrable Systems, Fluid Dynamics, 35C05, 35Q35;

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http://salesiana.dossiersoluciones.com/handle/123456789/174883

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0811.3724
 http://arxiv.org/abs/0811.3724

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arXiv