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Asymptotic Analysis of Nonlinear Wave Resonance
From lasers and medical imaging to earthquakes and epidemiology, resonance in nonlinear wave systems is a ubiquitous phenomenon leading to either potentially beneficial or detrimental outcomes. Given the complexity of the underlying mathematical models, asymptotic analysis can provide a powerful means for determining key features such as the amplification, response profiles, and dependence upon intrinsic model parameters. In this talk I will provide an overview of how a modally based approach can yield insights into such questions in the context of a general class of weakly forced nonlinear wave problems, with specific example in the context of gas dynamics. I will also show how an internal boundary layer approach may be applied in problems where forcing is strong and small parameters are present elsewhere, with an example in the context of waves in a shallow fluid.