Integration of non-Abelian Langmuir type lattices by the inverse spectral problem method

DOI10.1007/BF02466009zbMath0907.34047MaRDI QIDQ1392319

A. S. Osipov

Publication date: 11 October 1998

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

zbMATH Keywords

Korteweg-de Vries equationCauchy problemsLax representationbounded solutionsLangmuir chain

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear differential equations in abstract spaces (34G20) Inverse scattering problems in quantum theory (81U40)

Related Items (10)

Deficiency indices of block Jacobi matrices and Miura transformation ⋮ Inverse spectral problem for band operators and their sparsity criterion in terms of inverse problem data ⋮ Methods of evaluation and scale of functional spaces ⋮ On Weyl-Titchmarsh theory for singular finite difference Hamiltonian systems ⋮ An inverse spectral problem for a special class of band matrices and Bogoyavlensky lattice ⋮ Miura type transform between non-abelian Volterra and Toda lattices and inverse spectral problem for band operators ⋮ On the Links between Miura Transformations of Bogoyavlensky Lattices and Inverse Spectral Problems for Band Operators ⋮ The theory of primary measurements after Poincaré-Ehrenfest for the nonstationary Schrödinger equation ⋮ Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators ⋮ On some issues related to the moment problem for the band matrices with operator elements.

Cites Work

• Highest weight representations of the Lie algebra \(\mathfrak{gl}_{\infty}\)
• The integration of semi-infinite Toda chain by means of inverse spectral problem
• On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices

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