The defocusing nonlinear Schrödinger equation with t-periodic data: New exact solutions. (October 2015)

• Record Type: Journal Article
• Authors: Lenells, Jonatan
• Is Part Of: Nonlinear analysis. Volume 25(2015)
• Page Start: 31
• Page End: 50
• Publication Date: 2015-10
• Subjects: Initial–boundary value problem -- Time-periodic data -- Asymptotic behavior; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.02.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider solutions of the defocusing nonlinear Schrödinger (NLS) equation on the half-line whose Dirichlet and Neumann boundary values become periodic for sufficiently large t . We prove a theorem which, modulo certain assumptions, characterizes the pairs of periodic functions which can arise as Dirichlet and Neumann values for large t in this way. The theorem also provides a constructive way of determining explicit solutions with the given periodic boundary values. Hence our approach leads to a class of new exact solutions of the defocusing NLS equation on the half-line.