# The short pulse hierarchy

## 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.

- Authors:

- Departamento de Fisica, CFM Universidade Federal de Santa Catarina, Campus Universitario, Trindade, C.P. 476 CEP 88040-900 Florianopolis, SC (Brazil)

- Publication Date:

- OSTI Identifier:
- 20768699

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 46; Journal Issue: 12; Other Information: DOI: 10.1063/1.2146189; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EVOLUTION; HAMILTONIANS; INTEGRAL CALCULUS; LAX THEOREM; NONLINEAR PROBLEMS; OSCILLATIONS; PULSES; SCHROEDINGER EQUATION

### Citation Formats

```
Brunelli, J.C.
```*The short pulse hierarchy*. United States: N. p., 2005.
Web. doi:10.1063/1.2146189.

```
Brunelli, J.C.
```*The short pulse hierarchy*. United States. doi:10.1063/1.2146189.

```
Brunelli, J.C. Thu .
"The short pulse hierarchy". United States.
doi:10.1063/1.2146189.
```

```
@article{osti_20768699,
```

title = {The short pulse hierarchy},

author = {Brunelli, J.C.},

abstractNote = {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.},

doi = {10.1063/1.2146189},

journal = {Journal of Mathematical Physics},

number = 12,

volume = 46,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}

DOI: 10.1063/1.2146189

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