Alterman, Deborah; Rauch, Jeffrey Diffractive nonlinear geometric optics for short pulses. (English) Zbl 1036.35049 SIAM J. Math. Anal. 34, No. 6, 1477-1502 (2003). The paper deals with semilinear systems of hyperbolic partial differential equations on the time scale \(t= O(1/\varepsilon)\) being \(\varepsilon\ll 1\), the length of the pulse-like solutions. The amplitude is chosen so that nonlinear effects influence the leading term in the asymptotics. For pulses of larger amplitude so that the nonlinear effects are pertinent for times \(t= O(1)\), accurate asymptotic solutions lead to transport equations similar to those valid in the case of wave trains. The opposite is true in the studied case. The profile equation for pulses for \(t= O(1/\varepsilon)\) is different from the associated equation for wave trains. Reviewer: Luis Vazquez (Madrid) Cited in 15 Documents MSC: 35C20 Asymptotic expansions of solutions to PDEs 78A05 Geometric optics 35L60 First-order nonlinear hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:diffraction; short wavelength asymptotics PDFBibTeX XMLCite \textit{D. Alterman} and \textit{J. Rauch}, SIAM J. Math. Anal. 34, No. 6, 1477--1502 (2003; Zbl 1036.35049) Full Text: DOI