The dispersionless integrable systems and related conformal structure generating equations of mathematical physics

EasyChair Preprint no. 624, version 1

Abstract

Based on the vector fields on the complexified torus and the related Lie-algebraic structures, we devise an approach to constructing multidimensional dispersionless integrable systems, describing conformal structure generating equations of mathematical physics. As examples, we have analyzed Einstein--Weyl metric equation, the modified Einstein--Weyl metric equation, the Dunajski heavenly equations, first and second conformal structure generating equations, inverse first Shabat reduction heavenly equation, first Plebański heavenly equation, modified Plebański equation and  Husain heavenly equation.

Keyphrases: Casimir invariants, conformal structures, Hamiltonian system, heavenly equations, Lax--Sato equations, Lie-algebraic scheme, Lie-Poisson structure

@Booklet{EasyChair:624,
  author = {Oksana Hentosh and Yarema Prykarpatsky and Denis Blackmore and Anatolij Prykarpatski},
  title = {The dispersionless integrable  systems and related conformal structure generating equations of mathematical physics},
  howpublished = {EasyChair Preprint no. 624},

  year = {EasyChair, 2018}}