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TMF, 2009, Volume 159, Number 3, Pages 364–378 (Mi tmf6356)  

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

Building an extended resolvent of the heat operator via twisting transformations

M. Boitia, F. Pempinellia, A. K. Pogrebkovb, B. Prinaria

a Lecce University
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We introduce twisting transformations for the heat operator. By the simultaneous use of these transformations, $N$ solitons are superimposed à la Darboux on a generic smooth potential decaying at infinity, and the corresponding Jost solutions are generated. We also use these twisting operators to study the existence of the related extended resolvent. We study the existence and uniqueness of the extended resolvent in detail in the case of $N$ solitons with $N$ "incoming" rays and one "outgoing" ray.

Keywords: Darboux transformation, multidimensional soliton, annihilator

DOI: https://doi.org/10.4213/tmf6356

Full text: PDF file (457 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 159:3, 721–733

Bibliographic databases:

Document Type: Article

Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “Building an extended resolvent of the heat operator via twisting transformations”, TMF, 159:3 (2009), 364–378; Theoret. and Math. Phys., 159:3 (2009), 721–733

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf6356
  • http://mi.mathnet.ru/eng/tmf/v159/i3/p364

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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. M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “The equivalence of different approaches for generating multisoliton solutions of the KPII equation”, Theoret. and Math. Phys., 165:1 (2010), 1237–1255  mathnet  crossref  crossref  adsnasa  isi
    2. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Properties of the solitonic potentials of the heat operator”, Theoret. and Math. Phys., 168:1 (2011), 865–874  mathnet  crossref  crossref  mathscinet  isi
    3. Boiti M., Pempinelli F., Pogrebkov A.K., “Heat operator with pure soliton potential: Properties of Jost and dual Jost solutions”, J Math Phys, 52:8 (2011), 083506  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    4. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Extended resolvent of the heat operator with a multisoliton potential”, Theoret. and Math. Phys., 172:2 (2012), 1037–1051  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    5. Zarmi Ya., “Nonlinear Quantum-Dynamical System Based on the Kadomtsev-Petviashvili II Equation”, J. Math. Phys., 54:6 (2013), 063515  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Cauchy–Jost function and hierarchy of integrable equations”, Theoret. and Math. Phys., 185:2 (2015), 1599–1613  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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