The inverse scattering transform and squared eigenfunctions for the nondegenerate 3 × 3 operator and its soliton structure

DOI10.1088/0266-5611/26/5/055005zbMath1204.47011OpenAlexW2137026826MaRDI QIDQ3565181

Publication date: 2 June 2010

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/26/5/055005

zbMATH Keywords

inverse scattering transform eigenvalue problems Lax pair soliton structure three wave resonant interaction

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Scattering theory for PDEs (35P25) Eigenvalue problems for linear operators (47A75) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Scattering theory of linear operators (47A40) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (6)

Three-Wave Interaction Equations: Classical and Nonlocal ⋮ Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions ⋮ Geometric methods to investigate prolongation structures for differential systems with applications to integrable systems ⋮ Resonant solitons from the \(3 \times 3\) operator ⋮ Method for constructing analytical solutions to the Dym initial value problem ⋮ Semiclassical soliton ensembles for the three-wave resonant interaction equations

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