Mathematical Sciences: Asymptotic Methods For Nonlinear Waves

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This research will examine high-frequency nonlinear waves with applications to problems in continuum mechanics. Asymptotic methodology will be developed to analyze hyperbolic waves in several space dimensions and resonant wave-wave interactions. Application areas include mach configurations in reflected, focusing, and refracted shocks, nonlinear caustics, resonant interaction of sawtoothed waves, passage through resonance of nonlinear waves, nondispersive surface waves, and weakly dispersive short waves.