The Short Pulse Hierarchy
Exactly Solvable and Integrable Systems
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.nlin/0601015,
title = {The Short Pulse Hierarchy},
author = {Jose Carlos Brunelli},
journal= {arXiv preprint arXiv:nlin/0601015},
year = {2007}
}
Comments
Latex file, 13 pages, to appear in the Journal of Mathematical Physics