Nonvanishing at spatial extremity solutions of the defocusing nonlinear Schrödinger equation. (27th September 2018)

• Record Type: Journal Article
• Authors: Gialelis, Nikolaos; Stratis, Ioannis G.
• Other Names: Kravchenko Vladislav V. guestEditor.; Porter R. Michael guestEditor.; Torba Sergii M. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 15(2019)
• Page Start: 4939
• Page End: 4956
• Publication Date: 2018-09-27
• Subjects: Cauchy problem -- dark soliton -- defocusing -- extension operator -- nonlinear Schrödinger equation -- nonvanishing at spatial extremity solutions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5074
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : We show local existence of certain type of solutions for the Cauchy problem of the defocusing nonlinear Schrödinger equation with pure power nonlinearity, in various cases of open sets, unbounded or bounded. These solutions do not vanish at the boundary or at infinity. We also show, in certain cases, that these solutions are unique and global.