Joly, J. L.; Métivier, G.; Rauch, J. On the profiles of nonlinear geometric optics. (English) Zbl 0891.35080 Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau Sémin. 1992-1993, Exp. No. 1, 14 p. (1993). The authors consider nonlinear evolution equations arising in geometric optics in one space variable and their asymptotic expansions [A. Majda and R. Rosales, Stud. Appl. Math. 71, 149-179 (1984; Zbl 0572.76066)] when the wave amplitude is small. The coefficient in the leading term of such an expansion satisfies the profile equation. The authors study the profile equations corresponding to certain systems of nonlinear, first-order, hyperbolic partial differential equations with the aim of analyzing the high-frequency solutions of the latter equations. Reviewer: T.Aktosun (Fargo) MSC: 35L40 First-order hyperbolic systems 35C20 Asymptotic expansions of solutions to PDEs 35L60 First-order nonlinear hyperbolic equations 78A05 Geometric optics Keywords:profile equation; high-frequency solutions Citations:Zbl 0572.76006; Zbl 0572.76066 PDFBibTeX XMLCite \textit{J. L. Joly} et al., Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau, Exp. No. 1, 14 p. (1993; Zbl 0891.35080) Full Text: EuDML