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Citation - WoS: 5
Citation - Scopus: 7
Solution of the Finite Complex Toda Lattice by the Method of Inverse Spectral Problem
(Elsevier Science inc, 2013) Huseynov, Aydin; Guseinov, Gusein Sh.
We show that the finite Toda lattice with complex-valued initial data can be integrated by the method of inverse spectral problem. For this goal spectral data for complex Jacobi matrices are introduced and an inverse spectral problem with respect to the spectral data is solved. The time evolution of the spectral data for the Jacobi matrix associated with the solution of the Toda lattice is computed. Using the solution of the inverse spectral problem with respect to the time-dependent spectral data we reconstruct the time-dependent Jacobi matrix and hence the desired solution of the finite complex Toda lattice. (C) 2012 Elsevier Inc. All rights reserved.
Citation - WoS: 3
Citation - Scopus: 3
A Class of Complex Solutions To the Finite Toda Lattice
(Pergamon-elsevier Science Ltd, 2013) Guseinov, Gusein Sh.
In this paper, a class of complex-valued solutions to the finite Toda lattice is constructed by using the inverse spectral method. The corresponding Lax operator is a finite complex Jacobi matrix. As the initial values there are taken such complex numbers that the corresponding Jacobi matrix has a simple spectrum. Some examples are given. (C) 2012 Elsevier Ltd. All rights reserved.