Hamiltonian Structure of Non-Abelian Toda Lattice

Keywords

Complex system, Mathematics, Physics, Mathematical physics, Computer science

References

• Separation of variables in the classicalSL(N) magnetic chainM. Gekhtman — 1995
• Hamiltonian methods in the theory of solitonsL. D. Faddeev, Leon A. Takhtajan — 1987
• The Toda flow on a generic orbit is integrablePercy Deift, L. C. Li, T. Nanda — 1984
• Integrable Hamiltonian systems connected with graded Lie algebrasA. G. Reiman — 1982
• Classical functional Bethe ansatz for SL(N): Separation of variables for the magnetic chainD. R. D. Scott — 1994
• Isospectral Hamiltonian flows in finite and infinite dimensionsMalcolm R. Adams, J. Harnad, Jacques Hurtubise — 1990
• The solution to a generalized Toda lattice and representation theoryBertram Kostant — 1979
• Darboux coordinates and Liouville-Arnold integration in loop algebrasM. R. Adams, J. Harnad, J. Hurtubise — 1992
• NonAbelian nonlinear lattice equations on finite intervalM. Gekhtman — 1993
• Inverse problem of the spectral analysis and non-Abelian chains of nonlinear equationsYu. M. Berezanskiĭ, M. Gekhtman — 1990
• Factorization of differential operators, quasideterminants, and nonabelian Toda field equationsPavel Etingof, Israel M. Gelfand, Vladimir Retakh — 1997
• Integration of some chains of nonlinear difference equations by the method of the inverse spectral problemYu. M. Berezanskiĭ, M. Gekhtman, Michael Shmoish — 1986
• Solution of infinite Toda chainsM. Gekhtman — 1991
• Systems of Toda type, inverse spectral problems, and representation theoryWilliam W. Symes — 1980
• On generalized spectral functions, the parametrization of block Hankel and block Jacobi matrices, and some root location problemsMichael Shmoish — 1994
• The nonabelian Toda lattice: Discrete analogue of the matrix Schrödinger spectral problemM. Bruschi, S. V. Manakov, O. Ragnisco — 1980
• The integration of semi-infinite toda chain by means of inverse spectral problemYu.M. Berezanski — 1986
• Expansions in eigenfunctions of selfadjoint operatorsЮ. М. Березанский, Richard Bolstein — 1968
• Toda flows, inverse spectral transform and realization theoryR.W. Brockett, L.W. Baybusovich — 1991
• The toda flow on a generic orbit is integrablePercy Deift, L.‐C. Li, T. Nanda — 1986

Cited by

• Discrete canonical system and non‐Abelian Toda lattice: Bäcklund–Darboux transformation, Weyl functions, and explicit solutionsA. L. Sakhnovich — 2003
• SPECTRAL ANALYSIS OF THE GENERALIZED SURFACE MARYLAND MODELF. Bentosela, Philippe Briet, L. А. Pastur — 2005
• Bi-differential calculi and integrable modelsAristophanes Dimakis, Folkert Müller-Hoissen — 1999
• Qualitative behavior of non-Abelian Toda-like flowsMelinda E. Koelling, Anthony M. Bloch, Michael Gekhtman — 2004
• Matrix-valued orthogonal polynomials on the real line: some extensions of the classical theoryL Miranian — 2005
• Lie algebraic aspects of the finite nonperiodic Toda flowsAnthony M. Bloch, Michael Gekhtman — 2007
• Matrix-valued Gegenbauer polynomialsErik Koelink, Ana M. de los Ríos, Pablo Román — 2014
• Sasakian quiver gauge theories and instantons on Calabi-Yau conesOlaf Lechtenfeld, Alexander D. Popov, Richard J. Szabo — 2014
• The spectra of the surface Maryland model for all phasesWencai Liu — 2016
• Inverse moment problem for non-Abelian Coxeter double Bruhat cellsMichael Gekhtman — 2016
• Arithmetic Spectral Transitions for the Maryland ModelSvetlana Jitomirskaya, Wencai Liu — 2016
• Matrix-Valued Gegenbauer-Type PolynomialsErik Koelink, Ana M. de los Ríos, Pablo Román — 2017
• Generalized Burchnall-Type Identities for Orthogonal Polynomials and ExpansionsMourad E. H. Ismail, Erik Koelink, Pablo Román — 2018
• Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda latticeMourad E. H. Ismail, Erik Koelink, Pablo Román — 2018
• Ladder relations for a class of matrix valued orthogonal polynomialsAlfredo Deaño, Bruno Eijsvoogel, Pablo Román — 2019
• Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z-graded graphsGamal Mograby, Maxim Derevyagin, Gerald V. Dunne — 2020
• Inverse Spectral Problems for Second-Order Difference Operators and Their Application to the Study of Volterra Type SystemsAndrey Osipov — 2020
• Orthogonal functions related to Lax pairs in Lie algebrasWolter Groenevelt, Erik Koelink — 2020
• Miura Type Transform Between Non-Abelian Volterra and Toda Lattices and Inverse Spectral Problem for Band OperatorsAlexander V. Osipov — 2023
• Non-Abelian Toda-type equations and matrix valued orthogonal polynomialsAlfredo Deaño, Lucía Morey, Pablo Román — 2023

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