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Brunelli, J. C.

The bi-Hamiltonian structure of the short pulse equation. (English) Zbl 1181.37094

Phys. Lett., A 353, No. 6, 475-478 (2006).
Summary: We prove the integrability of the short pulse equation derived recently by Schäfer and Wayne from a Hamiltonian point of view. We give its bi-Hamiltonian structure and show how the recursion operator defined by the Hamiltonian operators is connected with the one obtained by Sakovich and Sakovich. An alternative zero-curvature formulation is also given.

Cited in 1 Review
Cited in 66 Documents

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
78A60 Lasers, masers, optical bistability, nonlinear optics
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

integrable models; short pulse equation; bi-Hamiltonian systems; zero-curvature formulation

Software:

PSEUDO
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References:

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