A family of (2+1)-dimensional hydrodynamic type systems possessing pseudopotential

2007/04/26 by Alexander Odesskii, Odesskii, Alexander · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #hep-th #math-ph #math.AP #math.MP #msc:14H70 #msc:17B63 #msc:17B80 #msc:32L81 #nlin.SI

paper · pdf · doi:10.48550/arxiv.0704.3577

16 pages, latex

arxiv created 2007/06/01 · arxiv updated 2009/12/01

Abstract

We construct a family of integrable hydrodynamic type systems with three independent and n>1 dependent variables in terms of solutions of linear system of PDEs with rational coefficients. We choose the existence of a pseudopotential as a criterion of integrability. In the case n=2 this family is a general solution of the classification problem for such systems. We give also an elliptic analog of this family in the case n>2.

Cited by

• Integrable pseudopotentials related to elliptic curves
• Integrable pseudopotentials related to generalized hypergeometric functions
• Second order quasilinear PDEs and conformal structures in projective space

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