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D. Pelinovsky and G. Schneider

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Rigorous justification of the short-pulse equation

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Nonlinear Differential Equations and Applications 20, 1277-1294 (2013)

**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**:

short-pulse equation, Maxwell equations, justification analysis,
apriori energy estimates, local well-posedness.