Journal article Open Access

Solvability of the Direct and Inverse Problems for the Nonlinear Schrödinger Equation

Mark J. Ablowitz; Barbara Prinari; Javier Villarroel

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.

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Publication date:
May 1, 2005
DOI:
10.1007/s10440-005-1160-y

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