| Abstract: |
| In this talk we shall focus on the advancement of the Unified Transform Method of Fokas for solving the initial-boundary value problem (ibvp) of nonlinear evolution equations in one and two space dimensions. Although introduced as the ibvp analogue of the renowned Inverse Scattering Transform method for integrable nonlinear evolution equations, Fokas` approach can also be used to produce novel solution formulas for the linear versions of such equations. Replacing in Fokas` solution formulas the forcing with the nonlinearity provides a new framework for the analysis of nonlinear equations with a variety of boundary conditions in appropriate solution spaces. The nonlinear Schr\odinger equation and Korteweg-de Vries equation will be at the center of our discussion, and it will be based on collaborative work with Athanassios Fokas, Dionyssis Mantzavinos and Fangchi Yan. |
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