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

• Alexander Odesskii ^[1]
  1. [1] University of Manchester

     University of Manchester

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 4, 2008, págs. 727-742
• Idioma: inglés
• DOI: 10.1007/s00029-008-0050-3
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• Resumen

  • We construct a family of integrable hydrodynamic type systems with three independent and n ≥ 2 dependent variables in terms of solutions of a 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 also give an elliptic analog of this family in the case n > 2.