A class of complex solutions to the finite Toda lattice

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Date

2013

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Pergamon-elsevier Science Ltd

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

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.

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Keywords

Toda lattice, Jacobi matrix, Difference equation, Spectral data, Inverse spectral problem

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Citation

4

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Volume

57

Issue

5-6

Start Page

1190

End Page

1202

URI

https://doi.org/10.1016/j.mcm.2012.10.022
 https://hdl.handle.net/20.500.14411/459

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