On the Darboux transform and the solutions of some integrable systems

The relation between the concept of Darboux transform and the full Kostant Toda lattice is analyzed. The main result is Theorem 1 , where the discrete Korteweg de Vries equation is used to obtain new solutions of the full Kostant Toda lattice. In addition, an iterative method to obtain the generaliz...

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Bibliographic Details
Published inRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Vol. 113; no. 2; pp. 1359 - 1378
Main Author Rolanía, D. Barrios
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2019
Subjects
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
Hessenberg banded matrices
30E10
Integrable systems
Darboux transforms
15A23
39A70
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Summary:The relation between the concept of Darboux transform and the full Kostant Toda lattice is analyzed. The main result is Theorem 1 , where the discrete Korteweg de Vries equation is used to obtain new solutions of the full Kostant Toda lattice. In addition, an iterative method to obtain the generalized Darboux factorization for a Hessenberg banded matrix is provided, which is the basis to obtain the new solutions.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-018-0553-5