An analog of the Fourier transform associated with a nonlinear one-dimensional Schrödinger equation

DOI10.1016/S0362-546X(02)00130-XzbMath1025.34087MaRDI QIDQ1863467

Peter E. Zhidkov

Publication date: 11 March 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

zbMATH Keywords

Fourier transformcontinuous spectrumcompleteness of eigenfunctionseigenfunction expanionnonlinear Schrödinger equation on half line

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Nonlinear ordinary differential operators (34L30)

Related Items (1)

On the eigenfunction expansions associated with semilinear Sturm-Liouville-type problems

Cites Work

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• On the Completeness of the System of Normalized Eigenfunctions of a Nonlinear Schrödinger-Type Operator on a Segment
• Completeness of systems of eigenfunctions for the Sturm-Liouville operator with potential depending on the spectral parameter and for one non-linear problem
• Riesz basis property of the system of eigenfunctions for a non-linear problem of Sturm-Liouville type
• On the property of being a basis for a denumerable set of solutions of a nonlinear Schrödinger-type boundary-value problem
• Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory

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