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TMF, 2011, Volume 168, Number 1, Pages 13–23 (Mi tmf6660)  

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

Properties of the solitonic potentials of the heat operator

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

a Dipartimento di Fisica, Università del Salento and Sezione INFN, Lecce, Italy
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: We study properties of the purely solitonic $\tau$-function and potential of the heat equation in detail. We describe the asymptotic behavior of the potential and establish the ray structure of this asymptotic behavior on the plane $(x_1,x_2)$ in dependence on the parameters of the potential.

Keywords: Kadomtsev–Petviashvili equation, soliton, asymptotic potential

DOI: https://doi.org/10.4213/tmf6660

Full text: PDF file (446 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 168:1, 865–874

Bibliographic databases:

Document Type: Article

Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Properties of the solitonic potentials of the heat operator”, TMF, 168:1 (2011), 13–23; Theoret. and Math. Phys., 168:1 (2011), 865–874

Citation in format AMSBIB
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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. 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
    2. 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
    3. 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
    4. Zarmi Ya., “Vertex Dynamics in Multi-Soliton Solutions of Kadomtsev-Petviashvili II Equation”, Nonlinearity, 27:6 (2014), 1499–1523  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. Boiti M. Pempinelli F. Pogrebkov A.K., “Kpii: Cauchy-Jost Function, Darboux Transformations and Totally Nonnegative Matrices”, J. Phys. A-Math. Theor., 50:30 (2017), 304001  crossref  mathscinet  zmath  isi  scopus
    6. Abenda S., Grinevich P.G., “Rational Degenerations of -Curves, Totally Positive Grassmannians and KP2-Solitons”, Commun. Math. Phys., 361:3 (2018), 1029–1081  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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