| Abstract: |
| In this talk we focus on the generalized Dirichlet-to-Neumann map, i.e. the problem of determining the unknown boundary values in terms of the given initial and boundary conditions, for linear and nonlinear integrable evolution equations including the nonlinear Schroedinger (NLS) equation, the Korteweg-de Vries equation and the modified Korteweg-de Vries equation. We revisit a method that appeared in $[1]$ for the NLS equation with time-periodic boundary data, extend the results, and show the power of the Lax pair formulation even in the case of linear problems. This is joint work with my PhD supervisor Prof. A.S. Fokas.
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$[1]$ J. Lenells and A.S. Fokas, {\it The Nonlinear Schroedinger Equation with t-Periodic Data: II. Perturbative Results}, Proc. R. Soc. A {\bf 471}, 20140926 (2015). |
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