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2012 | OriginalPaper | Chapter

Time Evolution of the Spectral Data Associated with the Finite Complex Toda Lattice

Authors : Aydin Huseynov, Gusein Sh. Guseinov

Published in: Dynamical Systems and Methods

Publisher: Springer New York

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Abstract

Spectral data for complex Jacobi matrices are introduced and the time evolution of the spectral data for the Jacobi matrix associated with the solution of the finite complex Toda lattice is computed.

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previous chapter Exciton–Phonon Dynamics with Long-Range Interaction
next chapter Efficient Dynamic Modeling of a Hexa-Type Parallel Manipulator
Literature
1.
Kac M, van Moerbeke P (1975) On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices. Adv Math 16:160–169MATHCrossRef
2.
Moser J (1975) Three integrable Hamiltonian systems connected with isospectral deformations. Adv Math 16:197–220MATHCrossRef
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Teschl G (2000) Jacobi operators and completely integrable nonlinear lattices. In: Math. surveys monographs, vol 72. American Mathematical Society, Providence
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Berezanskii Yu M, Mokhonko AA (2008) Integration of some differential-difference nonlinear equations using the spectral theory of normal block Jacobi matrices. Funct Anal Appl 42:1–18CrossRef
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Huseynov A (2008) On solutions of a nonlinear boundary value problem for difference equations. Trans Natl Acad Sci Azerb Ser Phys-Tech Math Sci 28(4):43–50MathSciNetMATH
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Bereketoglu H, Huseynov A (2009) Boundary value problems for nonlinear second-order difference equations with impulse. Appl Math Mech (English Ed.) 30:1045–1054MathSciNetMATHCrossRef
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Huseynov A (2010) Positive solutions for nonlinear second-order differernce equations with impulse. Dyn Contin Discret Impuls Syst Ser A: Math Anal 17:115–132MathSciNetMATH
10.
Guseinov GSh (2009) Inverse spectral problems for tridiagonal N by N complex Hamiltonians. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5:1–28, Paper 018
Metadata
Title
Time Evolution of the Spectral Data Associated with the Finite Complex Toda Lattice
Authors
Aydin Huseynov
Gusein Sh. Guseinov
Copyright Year
2012
Publisher
Springer New York
Book
Dynamical Systems and Methods

Print ISBN: 978-1-4614-0453-8

Electronic ISBN: 978-1-4614-0454-5

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-1-4614-0454-5_19

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