Solvability of the direct and inverse problems for the nonlinear schrödinger equation

Javier Villarroel; Mark J. Ablowitz; Barbara Prinari

doi:10.1007/s10440-005-1160-y

Solvability of the direct and inverse problems for the nonlinear schrödinger equation

Javier Villarroel
, Mark J. Ablowitz
, Barbara Prinari

Mathematics

Universidad de Salamanca
University of Colorado Boulder

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schrödinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We identify functional spaces in which both direct and inverse problems are well posed, have a unique solution and the corresponding direct and inverse maps are one to one.

Original language	English
Pages (from-to)	245-280
Number of pages	36
Journal	Acta Applicandae Mathematicae
Volume	87
Issue number	1-3
DOIs	https://doi.org/10.1007/s10440-005-1160-y
State	Published - May 2005

Keywords

Nonlinear Schrödinger
Rigorous spectral theory

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10.1007/s10440-005-1160-y

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abstract = "In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schr{\"o}dinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We identify functional spaces in which both direct and inverse problems are well posed, have a unique solution and the corresponding direct and inverse maps are one to one.",

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AU - Villarroel, Javier

AU - Ablowitz, Mark J.

AU - Prinari, Barbara

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N2 - In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schrödinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We identify functional spaces in which both direct and inverse problems are well posed, have a unique solution and the corresponding direct and inverse maps are one to one.

AB - In this paper we study rigorous spectral theory and solvability for both the direct and inverse problems of the Dirac operator associated with the nonlinear Schrödinger equation. We review known results and techniques, as well as incorporating new ones, in a comprehensive, unified framework. We identify functional spaces in which both direct and inverse problems are well posed, have a unique solution and the corresponding direct and inverse maps are one to one.

KW - Nonlinear Schrödinger

KW - Rigorous spectral theory

UR - https://www.scopus.com/pages/publications/21044442166

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JO - Acta Applicandae Mathematicae

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ER -

Solvability of the direct and inverse problems for the nonlinear schrödinger equation

Abstract

Keywords

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