ABSTRACT
In this chapter, the authors analyse the resonant interaction of hyperbolic waves that are nondispersive. As a result they resonate much more easily than dispersive waves. The nonlinear distortion of the wave forms have to be determined simultaneously with the evolution of modulations in the wave amplitudes. The authors describe the extension to oblique plane wave interactions in several space dimensions and apply the general theory to gas dynamics. The interaction of hyperbolic surface waves leads to equations of the same form as the ones derived for hyperbolic waves in an unbounded medium. More generally, waves whose frequency and wavelength are much greater than or much smaller than any characteristic frequencies and length scales of the wave motion can satisfy asymptotically even if the full problem is not scale invariant.
