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On the Darboux transform and the solutions of some integrable systems

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

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.

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Acknowledgements

This work was partially supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad, under grant MTM2014-54053-P.

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Authors and Affiliations

  1. ETS Ingeniería Civil, Universidad Politécnica de Madrid, C/ Alfonso XII, 3 y 5, 28014, Madrid, Spain

    D. Barrios Rolanía

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  1. D. Barrios Rolanía
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Correspondence to D. Barrios Rolanía.

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Rolanía, D.B. On the Darboux transform and the solutions of some integrable systems. RACSAM 113, 1359–1378 (2019). https://doi.org/10.1007/s13398-018-0553-5

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  • DOI: https://doi.org/10.1007/s13398-018-0553-5

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