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Showing 1 to 5 of 5 for “"Unified Transform Method"”.
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Solution Of Linear Evolution Partial Differential Equations On The Half-Line
… implementation of new techniques, such as the Unified Transform method. Lastly, we examine how the Unified Transform method can be invoked to solve initial boundary value problems involving the linear Schrodinger and Airy equations.
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Continuous and quad-graph integrable models with a boundary: Reflection maps and 3D-boundary consistency
… (NLS) equation on the halfline. Using a Backlund transformation method which explores the folding symmetry of the system, classes of integrable boundary conditions (BCs) are derived. These BCs coincide with the linearizable BCs obtained using the unified transform method developed by Fokas. The …
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Analysis in Fractional Calculus and Asymptotics Related to Zeta Functions
… theorem, Malgrange-Ehrenpreis theorem, and unified transform method for fractional PDEs. Each one is analogous to a known result for classical PDEs, but the proof in the general fractional scenario requires new ideas and modifications. Fractional derivatives and integrals are not uniquely …
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Boundary Value Problems for the Laplace Equation on Convex Domains with Analytic Boundary
… boundary. This is done by introducing a new transform, denoted by F_p, that is an analogue of the Fourier transform on smooth convex curves. We show that the F_p-transform is a bounded and invertible integral operator. Following this, we show that the F_p-transform naturally arises in the …
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Integrable Evolution Partial Differential Equations: Multidimensions and Dirichlet-to-Neumann Maps
… the so-called Lax pair, and can be solved via a method related to the Inverse Scattering Transform. Although integrable systems are quite rare, they play an extremely important role in physical applications, including the theory of water waves and optics. The thesis focuses on two main topics: A. …