Abstract

The Inverse Scattering Transform (IST) for the defocusing vector nonlinear Schrodinger equations (NLS), with an arbitrary number of components and nonvanishing boundary conditions at space infinities, is formulated by adapting and generalizing the approach used by Beals, Deift, and Tomei in the development of the IST for the N-wave interaction equations. Specifically, a complete set of sectionally meromorphic eigenfunctions is obtained from a family of analytic forms that are constructed for this purpose. As in the scalar and two-component defocusing NLS, the direct and inverse problems are formulated on a two-sheeted, genus-zero Riemann surface, which is then transformed into the complex plane by means of an appropriate uniformization variable. The inverse problem is formulated as a matrix Riemann-Hilbert problem with prescribed poles, jumps, and symmetry conditions. In contrast to traditional formulations of the IST, the analytic forms and eigenfunctions are first defined for complex values of the scattering parameter, and extended to the continuous spectrum a posteriori.

Autore Pugliese

• Prinari Barbara

Tutti gli autori

• Prinari B. , Biondini G. , Trubatch A.D.

Titolo volume/Rivista

STUDIES IN APPLIED MATHEMATICS

Anno di pubblicazione

2011

ISSN

0022-2526

ISBN

Non Disponibile

Numero di citazioni Wos

15

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

15

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile