The Short Pulse Hierarchy

Details The Short Pulse Hierarchy The Short Pulse Hierarchy

2006-01-05

arxiv.org/abs/nlin/0601015v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Latex file, 13 pages, to appear in the Journal of Mathematical Physics

Scientific paper

We study a new hierarchy of equations containing the Short Pulse equation, which describes the evolution of very short pulses in nonlinear media, and the Elastic Beam equation, which describes nonlinear transverse oscillations of elastic beams under tension. We show that the hierarchy of equations is integrable. We obtain the two compatible Hamiltonian structures. We construct an infinite series of both local and nonlocal conserved charges. A Lax description is presented for both systems. For the Elastic Beam equations we also obtain a nonstandard Lax representation.

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