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

2011 ◽  
pp. 323-334 ◽  
Author(s):  
Aydin Huseynov ◽  
Gusein Sh. Guseinov
Keyword(s):  
Spectral Data ◽  
Time Evolution ◽  
Toda Lattice ◽  
Finite Complex

scholarly journals ON THE INTEGRATION OF A HIRERARCHY FOR THE PEREODIC TODA LATTICE WITH A FREE TERM

2021 ◽  
pp. 101-110
Keyword(s):  
Spectral Problem ◽  
Spectral Data ◽  
Time Evolution ◽  
Toda Lattice ◽  
Inverse Spectral Problem ◽  
Complete Integrability ◽  
Free Term ◽  
Periodic Functions ◽  
Periodic Coefficients ◽  
Toda Lattice Hierarchy

In this article, we have explored the Toda lattice hierarchy in the class of periodic functions with a free term. We have given an effective method of constructing of the periodic Toda lattice hierarchy with a free term. We have discussed the complete integrability of the constructed systems that is based on the inverse spectral problem of an associated discrete Hill`s equation with periodic coefficients. In particular, Dubrovin-type equations are derived for the time-evolution of the spectral data corresponding to the solutions of any system in the hierarchy.

scholarly journals On the Construction and Integration of a Hierarchy for the Periodic Toda Lattice with a Self-Consistent Source

2021 ◽  
Vol 38 ◽  
pp. 3-18
Author(s):  
B. A. Babajanov ◽  
◽  
M. M. Ruzmetov ◽  
Keyword(s):  
Spectral Data ◽  
Time Evolution ◽  
Toda Lattice ◽  
Complete Integrability ◽  
Numerical Results ◽  
Periodic Functions ◽  
Hill’S Equation ◽  
Periodic Coefficients ◽  
Hill's Equation ◽  
Self Consistent

In this paper, it is derived a rich hierarchy for the Toda lattice with a selfconsistent source in the class of periodic functions. We discuss the complete integrability of the constructed systems that is based on the transformation to the spectral data of an associated discrete Hill‘s equation with periodic coefficients. In particular, Dubrovintype equations are derived for the time-evolution of the spectral data corresponding to the solutions of any system in the hierarchy. At the end of the paper, we illustrate our theory on concrete example with analytical and numerical results.

Toda lattice with corrections via inverse scattering transform

2020 ◽  
pp. 2150084
Author(s):  
Yanpei Zhen ◽  
Xiaodan Wang ◽  
Junyi Zhu
Keyword(s):  
Perturbation Theory ◽  
Approximate Solution ◽  
Conservation Laws ◽  
Time Evolution ◽  
Inverse Scattering ◽  
Toda Lattice ◽  
Inverse Scattering Transform ◽  
Scattering Data ◽  
Scattering Transform

The perturbation theory based on the inverse scattering transform is extended to discuss the Toda lattice with corrections. The time evolution of the associated scattering data is given by some summation representations for corrections and eigenfunctions. The perturbation correction of the conservation laws is investigated. The adiabatic approximate solution and its correction are considered.

Estimating Pigment Concentrations from Spectral Images Using an Encoder‐Decoder Neural Network

2020 ◽  
Vol 64 (3) ◽  
pp. 30502-1-30502-15
Author(s):  
Kensuke Fukumoto ◽  
Norimichi Tsumura ◽  
Roy Berns
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Absorption Coefficient ◽  
Spectral Data ◽  
High Accuracy ◽  
Pigment Concentration ◽  
Scattering Coefficient ◽  
A Value ◽  
Input And Output ◽  
Pigment Concentrations

Abstract A method is proposed to estimate the concentration of pigments mixed in a painting, using the encoder‐decoder model of neural networks. The model is trained to output a value that is the same as its input, and its middle output extracts a certain feature as compressed information about the input. In this instance, the input and output are spectral data of a painting. The model is trained with pigment concentration as the middle output. A dataset containing the scattering coefficient and absorption coefficient of each of 19 pigments was used. The Kubelka‐Munk theory was applied to the coefficients to obtain many patterns of synthetic spectral data, which were used for training. The proposed method was tested using spectral images of 33 paintings, which showed that the method estimates, with high accuracy, the concentrations that have a similar spectrum of the target pigments.

Detection of potential aircraft icing regions with GOES multi-spectral data

1997 ◽  
Author(s):  
Gary Ellrod ◽  
James Nelson, III ◽  
Gary Ellrod ◽  
James Nelson, III
Keyword(s):  
Spectral Data ◽  
Aircraft Icing
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