Modal expansions and completeness relations for some time-dependent Schrödinger equations

DOI10.1016/S0167-2789(98)00147-XzbMath0939.35157OpenAlexW2155566684MaRDI QIDQ1808295

Peter D. Miller, Nail N. Akhmediev

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(98)00147-x

zbMATH Keywords

initial value problemcompleteness relationsmultisoliton interactions in the vector nonlinear Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30)

Related Items (2)

Darboux partners of pseudoscalar Dirac potentials associated with exceptional orthogonal polynomials ⋮ Nonlinear waves and solitons in physical systems

Cites Work

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• Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation
• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• Vector nonlinear Schrödinger hierarchies as approximate Kadomtsev-Petviashvili hierarchies
• Completeness of Derivatives of Squared Schrödinger Eigenfunctions and Explicit Solutions of the Linearized K<scp>d</scp>V Equation
• On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation
• Solutions to the Time Dependent Schrödinger and the Kadomtsev-Petviashvili Equations
• Periodic Optical Waveguides: Exact Floquet Theory and Spectral Properties

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