Analogs of multisoliton potentials for the two-dimensional Schrödinger operator

DOI10.1007/BF01077292zbMath0657.35122OpenAlexW1966831238MaRDI QIDQ1110740

Petr G. Grinevich, Roman G. Novikov

Publication date: 1985

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01077292

zbMATH Keywords

inverse problemSchrödinger operatorKorteweg-de Vries equationscattering amplitudemultisolitonnonlocal Riemann problem

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Schrödinger operator, Schrödinger equation (35J10) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (6)

On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator ⋮ Mapping Properties of the Nonlinear Fourier Transform in Dimension Two ⋮ Riemann–Hilbert problem approach for two-dimensional flow inverse scattering ⋮ Fast-decaying potentials on the finite-gap background and the \(\overline {\partial}\)-problem on the Riemann surfaces ⋮ The Novikov-Veselov equation and the inverse scattering method. I: Analysis ⋮ Two-dimensional stationary Schrödinger equation via the ∂¯-dressing method: New exactly solvable potentials, wave functions, and their physical interpretation

Cites Work

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• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• Multidimensional nonlinear integrable systems and methods for constructing their solutions

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