The inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonzero boundary conditions

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Abstract

A rigorous theory of the inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonvanishing boundary values is presented. The direct problem is shown to be well posed for potentials in a suitable functional class, for which analyticity properties of eigenfunctions and scattering data are established. The inverse scattering problem is formulated and solved both via Marchenko integral equations, and as a Riemann-Hilbert problem in terms of a suitable uniform variable. The asymptotic behavior of the scattering data is determined and shown to ensure the linear system solving the inverse problem is well defined. Finally, the triplet method is developed as a tool to obtain explicit multisoliton solutions by solving the Marchenko integral equation via separation of variables.

Autore Pugliese

Tutti gli autori

  • F. Demontis , B. Prinari , C. van der Mee , F. Vitale

Titolo volume/Rivista

STUDIES IN APPLIED MATHEMATICS

Anno di pubblicazione

2013

ISSN

1467-9590

ISBN

Non Disponibile

Numero di citazioni Wos

17

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

17

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile