Solution of a Schrödinger inverse scattering problem with a polynomial spectral dependence in the potential

DOI10.1063/1.525347zbMath0521.35013OpenAlexW2161121976MaRDI QIDQ3671572

Cecile Jean, Marcel Jaulent

Publication date: 1982

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.525347

zbMATH Keywords

inverse scattering problemscalar Schrödinger equationGelfand-Dikii method

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Inverse problems for PDEs (35R30) Schrödinger operator, Schrödinger equation (35J10) (2)-body potential quantum scattering theory (81U05) Scattering theory of linear operators (47A40)

Related Items (3)

INVERSE SCATTERING PROBLEM FOR THE ·IMPULSIVE SCHRÖDINGER EQUATION WITH A POLYNOMIAL SPECTRAL DEPENDENCE IN THE POTENTIAL ⋮ Transformation operators in controllability problems for the wave equations with variable coefficients on a half-axis controlled by the Dirichlet boundary condition ⋮ New direct linearizations for KdV and solutions of the other Cauchy problem

Cites Work

• Gel'fand-Dikii method and nonlinear equations associated to Schrödinger operators with energy-dependent potentials
• Nonlinear evolution equations associated with energy-dependent Schrödinger potentials
• On the Extension of Inverse Scattering Method
• Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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