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SIGMA, 2017, Volume 13, 010, 20 pp. (Mi sigma1210)  

This article is cited in 6 scientific papers (total in 6 papers)

Classification of Multidimensional Darboux Transformations: First Order and Continued Type

David Hobby, Ekaterina Shemyakova

1 Hawk dr., Department of Mathematics, State University of New York at New Paltz, USA

Abstract: We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a complete description of all possible first-order Darboux transformations. We introduce a large class of invertible Darboux transformations of higher order, which we call Darboux transformations of continued Type I. This generalizes the class of Darboux transformations of Type I, which was previously introduced. There is also a modification of this type of Darboux transformations, continued Wronskian type, which generalize Wronskian type Darboux transformations.

Keywords: Darboux transformations; Laplace transformations; linear partial differential operators; continued Darboux transformations.

DOI: https://doi.org/10.3842/SIGMA.2017.010

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Full text: http://www.emis.de/.../010
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Bibliographic databases:

ArXiv: 1605.04362
MSC: 16S32; 37K35; 37K25
Received: October 10, 2016; in final form February 14, 2017; Published online February 24, 2017
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Citation: David Hobby, Ekaterina Shemyakova, “Classification of Multidimensional Darboux Transformations: First Order and Continued Type”, SIGMA, 13 (2017), 010, 20 pp.

Citation in format AMSBIB
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\by David~Hobby, Ekaterina~Shemyakova
\paper Classification of Multidimensional Darboux Transformations: First~Order and Continued Type
\jour SIGMA
\yr 2017
\vol 13
\papernumber 010
\totalpages 20
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ch. Athorne, “Laplace maps and constraints for a class of third-order partial differential operators”, J. Phys. A-Math. Theor., 51:8 (2018), 085205  crossref  mathscinet  zmath  isi
    2. H. Riaz, A. Wajahat, M. Hassan, “On soliton solutions of multi-component semi-discrete short pulse equation”, J. Phys. Commun., 2:2 (2018), UNSP 025005  crossref  mathscinet  isi
    3. H. Riaz, A. Wajahat, M. Hassan, “Multi-component semi-discrete coupled dispersionless integrable system, its Lax pair and Darboux transformation”, Commun. Nonlinear Sci. Numer. Simul., 61 (2018), 71–83  crossref  mathscinet  isi
    4. S. V. Smirnov, “Factorization of Darboux–Laplace transformations for discrete hyperbolic operators”, Theoret. and Math. Phys., 199:2 (2019), 621–636  mathnet  crossref  crossref  adsnasa  isi  elib
    5. Shemyakova E., Voronov T., “Differential Operators on the Algebra of Densities and Factorization of the Generalized Sturm-Liouville Operator”, Lett. Math. Phys., 109:2 (2019), 403–421  crossref  mathscinet  zmath  isi  scopus
    6. Athorne Ch., Yilmaz H., “Twisted Laplace Maps”, J. Phys. A-Math. Theor., 52:22 (2019), 225201  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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