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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 3, Pages 364–378
DOI: https://doi.org/10.4213/tmf6356 (Mi tmf6356) 		 
This article is cited in 11 scientific papers (total in 11 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
Full-text PDF (457 kB) Citations (11)
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DOI: https://doi.org/10.4213/tmf6356
Abstract: We introduce twisting transformations for the heat operator. By the simultaneous use of these transformations, NN 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.
English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 3, Pages 721–733
DOI: https://doi.org/10.1007/s11232-009-0060-0
Bibliographic databases:
Document Type: Article
Language: Russian
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://www.mathnet.ru/eng/tmf/v159/i3/p364
    • This publication is cited in the following 11 articles:
    1. Derchyi Wu, “Stability of Kadomtsev–Petviashvili multi-line solitons”, Nonlinearity, 38:1 (2025), 015014  crossref
    2. Gino Biondini, Alexander J Bivolcic, Mark A Hoefer, Antonio Moro, “Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation”, Nonlinearity, 37:2 (2024), 025012  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
    5. Biondini G. Hoefer M.A. Moro A., “Integrability, Exact Reductions and Special Solutions of the Kp-Whitham Equations”, Nonlinearity, 33:8 (2020), 4114–4132  crossref  mathscinet  isi
    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
    7. 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
    8. 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
    9. 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
    10. 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
    11. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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