The short pulse hierarchy

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 i...

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Bibliographic Details
Published in:Journal of mathematical physics 2005-12, Vol.46 (12), p.123507-123507-9
Main Author: Brunelli, J. C.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EVOLUTION
Exact sciences and technology
HAMILTONIANS
INTEGRAL CALCULUS
LAX THEOREM
Mathematical methods in physics
Mathematics
NONLINEAR PROBLEMS
OSCILLATIONS
Physics
PULSES
SCHROEDINGER EQUATION
Sciences and techniques of general use
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2146189