Strongly nonlinear hyperbolic waves. (English) Zbl 0689.35083

Hunter, John K.

Nonlinear hyperbolic equations - theory, computation methods, and applications, Proc. 2nd Int. Conf., Aachen/FRG 1988, Notes Numer. Fluid Mech. 24, 257-268 (1989).

[For the entire collection see Zbl 0659.00008.]
This paper gives an overview of some aspects of geometrical optics theories for nonlinear hyperbolic systems of partial differential equations. Solutions with compactly supported initial data and with periodic initial data are considered. At the end an example for resonantly interacting sawtooth waves is discussed.

Reviewer: H.-D.Alber

MSC:

35Q99	Partial differential equations of mathematical physics and other areas of application
35L60	First-order nonlinear hyperbolic equations
78A40	Waves and radiation in optics and electromagnetic theory
35A30	Geometric theory, characteristics, transformations in context of PDEs

Keywords:

inviscid Burgers equation; periodic initial data