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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 172, Number 2, Pages 181–197
DOI: https://doi.org/10.4213/tmf6970 (Mi tmf6970) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Extended resolvent of the heat operator with a multisoliton potential

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

a Dipartimento di Fisica, Università del Salento and Sezione INFN, Lecce, Italy
b Steklov Mathematical Institute, RAS, Moscow, Russia
Full-text PDF (508 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf6970
Abstract: We consider the heat operator with a general multisoliton potential and derive its extended resolvent depending on a parameter q∈R2. We show that it is bounded in all variables and find its singularities in q. We introduce the Green's functions and study their properties in detail.
Keywords: Kadomtsev–Petviashvili equation, heat operator, extended resolvent, soliton.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00440
Ministry of Education and Science of the Russian Federation НШ-4612.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Instituto Nazionale di Fisica Nucleare
Italian Ministry of Education, University and Research PRIN 2008
Received: 13.03.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 172, Issue 2, Pages 1037–1051
DOI: https://doi.org/10.1007/s11232-012-0094-6
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, “Extended resolvent of the heat operator with a multisoliton potential”, TMF, 172:2 (2012), 181–197; Theoret. and Math. Phys., 172:2 (2012), 1037–1051
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6970
  • https://doi.org/10.4213/tmf6970
  • https://www.mathnet.ru/eng/tmf/v172/i2/p181
    • This publication is cited in the following 5 articles:
    1. Derchyi Wu, “Stability of Kadomtsev–Petviashvili multi-line solitons”, Nonlinearity, 38:1 (2025), 015014  crossref
    2. Tetsu Mizumachi, “Linear stability of elastic 2-line solitons for the KP-II equation”, Quart. Appl. Math., 82:1 (2023), 115  crossref
    3. Wu D., “The Direct Scattering Problem For Perturbed Kadomtsev-Petviashvili Multi Line Solitons”, J. Math. Phys., 62:9 (2021), 091513  crossref  mathscinet  isi
    4. Wu D., “The Direct Scattering Problem For the Perturbed Gr(1,2)(> 0)Kadomtsev-Petviash-Vili II Solitons”, Nonlinearity, 33:12 (2020), 6729–6759  crossref  mathscinet  isi  scopus
    5. A. K. Pogrebkov, “Hirota difference equation: Inverse scattering transform, Darboux transformation, and solitons”, Theoret. and Math. Phys., 181:3 (2014), 1585–1598  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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