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On the profiles of nonlinear geometric optics. (English) Zbl 0891.35080

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
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