Rigorous justification of the short-pulse equation
Mathematical Physics
2013-04-08 v2 Analysis of PDEs
math.MP
Pattern Formation and Solitons
Abstract
We prove that the short-pulse equation, which is derived from Maxwell equations with formal asymptotic methods, can be rigorously justified. The justification procedure applies to small-norm solutions of the short-pulse equation. Although the small-norm solutions exist for infinite times and include modulated pulses and their elastic interactions, the error bound for arbitrary initial data can only be controlled over finite time intervals.
Keywords
Cite
@article{arxiv.1108.5970,
title = {Rigorous justification of the short-pulse equation},
author = {Dmitry Pelinovsky and Guido Schneider},
journal= {arXiv preprint arXiv:1108.5970},
year = {2013}
}
Comments
15 pages, no figures