Multi-Hamiltonian structure of Plebanski's second heavenly equation

Details Multi-Hamiltonian structure of Plebanski's second heavenly equation Multi-Hamiltonian structure of Plebanski's second heavenly equation

2005-05-12

arxiv.org/abs/nlin/0505030v2

J.Phys. A38 (2005) 8473

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.1088/0305-4470/38/39/012

We show that Plebanski's second heavenly equation, when written as a
first-order nonlinear evolutionary system, admits multi-Hamiltonian structure.
Therefore by Magri's theorem it is a completely integrable system. Thus it is
an example of a completely integrable system in four dimensions.

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