D. Pelinovsky and G. Schneider

Rigorous justification of the short-pulse equation

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

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.

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