Mathematical Sciences: Nonlinear Wave Motion

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This project will develop coherent structures in nonlinear problems and obtain solutions to equations arising in physical problems. The techniques to be employed include asymptotic and perturbation analysis, numerical computation, and exact solutions. Especially important in the realm of exact analysis is the method of inverse scattering transform. This work has generic features and, consequently, broad applicability. Examples of applications include wave propagation in surface and internal waves, self focussing and soliton propagation in nonlinear optics, exact reductions of Einstein's vacuum equations, and aspects on numerical computation.