Browsing by Subject "Unified transform method"
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Item Open Access Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line(Element d.o.o., 2021-09) Özsarı, Türker; Alkan, Kıvılcım; Kalimeris, KonstantinosIn this paper, we prove dispersion estimates for the boundary integral operator associated with the fourth order Schr¨odinger equation posed on the half line. Proofs of such estimates for domains with boundaries are rare and generally require highly technical approaches, as opposed to our simple treatment which is based on constructing a boundary integral operator of oscillatory nature via the Fokas method. Our method is uniform and can be extended to other higher order partial differential equations where the main equation possibly involves more than one spatial derivatives.Item Open Access The interior-boundary Strichartz estimate for the Schrödinger equation on the half-line revisited(TÜBİTAK, 2022-01-01) Köksal, Bilge; Özsarı, TürkerIn recent papers, it was shown for the biharmonic Schrödinger equation and 2D Schrödinger equation that Fokas method-based formulas are capable of defining weak solutions of associated nonlinear initial boundary value problems (ibvps) below the Banach algebra threshold. In view of these results, we revisit the theory of interiorboundary Strichartz estimates for the Schrödinger equation posed on the right half line, considering both Dirichlet and Neumann cases. Finally, we apply these estimates to obtain low regularity solutions for the nonlinear Schrödinger equation (NLS) with Neumann boundary condition and a coupled system of NLS equations defined on the half line with Dirichlet/Neumann boundary conditions. © This work is licensed under a Creative Commons Attribution 4.0 International License.