Nonclassical symmetry reductions and exact solutions of the Zabolotskaya–Khokhlov equation

DOI10.1017/S0956792500000929zbMath0771.35053MaRDI QIDQ5286160

Simon Hood, Peter A. Clarkson

Publication date: 29 June 1993

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

direct methodAiry functionsWeber-Hermite functionsexact solutions in terms of Weierstrass zeta functions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Invariance and symmetry properties for PDEs on manifolds (58J70) Solutions to PDEs in closed form (35C05)

Related Items

Symmetry reductions and exact solutions of a class of nonlinear heat equations ⋮ New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations ⋮ Instantaneous blow-up of classical solutions to the Cauchy problem for the Khokhlov-Zabolotskaya equation ⋮ Special conditional similarity reductions and exact solutions of the \((2+1)\)-dimensional VCBKK system ⋮ The Cauchy problem for the Pavlov equation with large data ⋮ Some traveling wave solutions for the dissipative Zabolotskaya–Khokhlov equation ⋮ Nonlinear waves in materials with mixed nonlinearity. ⋮ Invariant solutions to the Khokhlov-Zabolotskaya singular manifold equation and their application ⋮ Extension to the direct methods and applications to the generalized Burgers equation ⋮ Nonclassical symmetry reductions of the Boussinesq equation ⋮ Nonclassical symmetry reductions of nonlinear partial differential equations

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