The short pulse hierarchy
By J. C. Brunelli. 2005
156 citations recorded by the source corpus.
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.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/eefebf5ed6a396faf747cf158e11a72ef3a117ae
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- B. Feng
- Anton Sakovich
- Sergei Sakovich
- Panayotis G. Kevrekidis
- Atanas Stefanov
- Bixiang Wang
- D. Tataru
In Statistical and Nonlinear Physics
- B. Feng
- J. C. Brunelli
- Anton Sakovich
- Sergei Sakovich
- Panayotis G. Kevrekidis
- Atanas Stefanov
- Yannan Shen
- Zuo-nong Zhu
Citations in the corpus
- Complex short pulse and coupled complex short pulse equations (2013, background): “onlinear optics, the SP equation has also been derived as an integrable differential equation associated with pseudospherical surfaces [11]. The SP equation has been shown to be completely integrable [11, 12, 13, 14, 15]. The periodic and soliton solutions of the SP equation were found in [16, 17, 1”
- Well-posedness and small data scattering for the generalized Ostrovsky equation ✩ (2010, background): “On the other hand, the short-pulse equation (SPE) proved to be extremely interesting from a mathematical point of view due to the existence of an infinite hierarchy of conserved quantities [10], an ingenious transformation that related it to the integrable sine-Gordon equation and illustrated its co”
- LETTER TO THE EDITOR: Solitary wave solutions of the short pulse equation (2006, background): “(3) Very recently, the bi-Hamiltonian structure of the SPE was discovered and the corresponding hierarchy and conservation laws were studied in [6, 7].”
- The bi-Hamiltonian structure of the short pulse equation (2006, background): “is exactly R obtained by Sakovich and Sacovich [4]. From the recursion operator (8) a whole hierarchy of equations and conserved charges can be constructed and the details will be published elsewhere [13]. However, since the system is bihamiltonian the SP equations and the other equations of the hie”