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Construction of solutions of the defocusing nonlinear Schrödinger equation with asymptotically time‐periodic boundary values
Author(s) -
Fromm Samuel
Publication year - 2019
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12285
Subject(s) - mathematics , mathematical analysis , nonlinear system , plane (geometry) , boundary (topology) , method of steepest descent , nonlinear schrödinger equation , exponential function , boundary value problem , schrödinger equation , geometry , physics , quantum mechanics
We study the defocusing nonlinear Schrödinger equation in the quarter plane with asymptotically periodic boundary values. We use the unified transform method, also known as the Fokas method, and the Deift‐Zhou nonlinear steepest descent method to construct solutions in a sector close to the boundary whose leading behavior is described by a single exponential plane wave. Furthermore, we compute the subleading terms in the long‐time asymptotics of the constructed solutions.