Abstract

We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrödinger (NLS) equation with initial conditions approaching constant values with the same amplitude as x approaches infinity. The theory combines and extends to a problem with non-zero boundary conditions three fundamental ideas: (i) the tensor approach used by Beals, Deift and Tomei for the n-th order scattering problem, (ii) the triangular decompositions of the scattering matrix used by Novikov, Manakov, Pitaevski and Zakharov for the N-wave interaction equations, and (iii) a generalization of the cross product via the Hodge star duality, which, to the best of our knowledge, is used in the context of the IST for the first time in this work. The combination of the first two ideas allows us to rigorously obtain a fundamental set of analytic eigenfunctions. The third idea allows us to establish the symmetries of the eigenfunctions and scattering data. The results are used to characterize the discrete spectrum and to obtain exact soliton solutions, which describe generalizations of the so-called dark-bright solitons of the two-component NLS equation.

Autore Pugliese

• Prinari Barbara

Tutti gli autori

• Biondini G. , Kraus D.K. , Prinari B.

Titolo volume/Rivista

COMMUNICATIONS IN MATHEMATICAL PHYSICS

Anno di pubblicazione

2016

ISSN

0010-3616

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

3

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile