The inverse scattering problems for the hyperbolic equations and their application to nonlinear integrable systems

DOI10.1016/0034-4877(88)90028-6zbMath0679.35086OpenAlexW2033088672MaRDI QIDQ1822697

Leonid P. Nizhnik

Publication date: 1988

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(88)90028-6

zbMATH Keywords

Cauchy probleminverse scatteringGlobal existencefactorization of the S- matrixhyperbolic Dirac system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Quantum scattering theory (81U99) First-order hyperbolic systems (35L40)

Related Items (12)

Transient waves in nonstationary media ⋮ Inverse scattering problem for nonstationary Dirac-type systems on the half-plane ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I ⋮ The inverse scattering problem for the perturbed string equation and its application to integration of the two-dimensional generalization from Korteweg-de Vries equation ⋮ Inverse nonstationary scattering for the linear system of the 3-wave interaction problem in the case of two incident waves with the same velocity ⋮ Inverse scattering transform in two spatial dimensions for the \(N\)-wave interaction problem with a dispersive term ⋮ Inverse scattering problem for nonstationary Dirac-type systems on the plane ⋮ Inverse scattering problem for linear system of four-wave interaction problem with equal number of incident and scattered waves ⋮ Theory of multidimensional Delsarte-Lions transmutation operators. II ⋮ ``The source problem -- Transient waves propagating from internal sources in non-stationary media ⋮ Theory of multidimensional Delsarte-Lions transmutation operators. I ⋮ Integration of nonlinear system of four waves with two velocities in (2 + 1) dimensions by the inverse scattering transform method

Cites Work

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• Integration of the nonlinear two-dimensional spatial Schrödinger equation by the inverse-problem method
• The inverse scattering solution for the full three dimensional three-wave resonant interaction
• On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
• Multidimensional Inverse Scattering for First-Order Systems
• Solutions of the generalized nonlinear Schrödinger equation in two spatial dimensions
• The inverse scattering transform: Semi-infinite interval
• On three-dimensional packets of surface waves
• Inverse nonstationary scattering problem for the Dirac equation

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