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.