Hydrodynamic reductions of the heavenly equation
Exactly Solvable and Integrable Systems
2009-11-10 v1 General Relativity and Quantum Cosmology
Abstract
We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.
Keywords
Cite
@article{arxiv.nlin/0301048,
title = {Hydrodynamic reductions of the heavenly equation},
author = {E. V. Ferapontov and M. V. Pavlov},
journal= {arXiv preprint arXiv:nlin/0301048},
year = {2009}
}
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14 pages