Rigorous justification of the short-pulse equation

Details Rigorous justification of the short-pulse equation Rigorous justification of the short-pulse equation

2011-08-30

arxiv.org/abs/1108.5970v1

Physics

Mathematical Physics

15 pages, no figures

Scientific paper

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.

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