Inverse scattering transform for the Toda hierarchy with quasi-periodic background

DOI10.1090/S0002-9939-06-08668-0zbMath1118.37034arXivnlin/0512003WikidataQ57343904 ScholiaQ57343904MaRDI QIDQ3430190

Johanna Michor, Iryna Egorova, Gerald Teschl

Publication date: 21 March 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0512003

zbMATH Keywords

periodic solutions

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory, inverse scattering involving ordinary differential operators (34L25) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (11)

Asymptotic periodic solution of the Cauchy problem for the Langmuir lattice ⋮ Scattering theory with finite-gap backgrounds: transformation operators and characteristic properties of scattering data ⋮ The Cauchy problem for a semi-infinite Volterra chain with an asymptotically periodic initial condition ⋮ Stability of periodic soliton equations under short range perturbations ⋮ An application of the inverse scattering problem for the discrete Dirac operator ⋮ Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds ⋮ Inverse scattering theory for one-dimensional Schrödinger operators with steplike finite-gap potentials ⋮ LONG-TIME ASYMPTOTICS OF THE TODA LATTICE FOR DECAYING INITIAL DATA REVISITED ⋮ Soliton solutions of the Toda hierarchy on quasi-periodic backgrounds revisited ⋮ On the Cauchy problem for the Korteweg-de Vries equation with steplike finite-gap initial data. II: Perturbations with finite moments ⋮ Long-time asymptotics of the periodic Toda lattice under short-range perturbations

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