M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “The equivalence of different approaches for generating multisoliton solutions of the KPII equation”, TMF, 165:1 (2010), 3–24; Theoret. and Math. Phys., 165:1 (2010), 1237

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 165, Number 1, Pages 3–24
DOI: https://doi.org/10.4213/tmf6560 (Mi tmf6560)

This article is cited in 16 scientific papers (total in 16 papers)

The equivalence of different approaches for generating multisoliton solutions of the KPII equation

M. Boiti^a, F. Pempinelli^a, A. K. Pogrebkov^b, B. Prinari^ac

^a Dipartimento di Fisica, Universitáa del Salento and Sezione, INFN, Lecce, Italy
^b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
^c Department of Mathematics, University of Colorado, Colorado Springs, USA

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DOI: https://doi.org/10.4213/tmf6560

Abstract: The unexpectedly rich structure of the multisoliton solutions of the KPII equation has previously been explored using different approaches ranging from the dressing method to twisting transformations and the

τ

$\tau$ -function formulation. All these approaches proved useful for displaying different properties of these solutions and the corresponding Jost solutions. The aim of our investigation is to establish explicit formulas relating all these approaches. We discuss some hidden invariance properties of these multisoliton solutions.

Keywords: KPII equation, Bäcklund transformation, tau function, soliton.

Received: 11.03.2010

English version:
Theoretical and Mathematical Physics, 2010, Volume 165, Issue 1, Pages 1237–1255
DOI: https://doi.org/10.1007/s11232-010-0106-3

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: M. Boiti, F. Pempinelli, A. K. Pogrebkov, B. Prinari, “The equivalence of different approaches for generating multisoliton solutions of the KPII equation”, TMF, 165:1 (2010), 3–24; Theoret. and Math. Phys., 165:1 (2010), 1237–1255

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https://doi.org/10.4213/tmf6560

https://www.mathnet.ru/eng/tmf/v165/i1/p3

This publication is cited in the following 16 articles:

Derchyi Wu, “Stability of Kadomtsev–Petviashvili multi-line solitons”, Nonlinearity, 38:1 (2025), 015014
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
Antonio Moro, Reference Module in Materials Science and Materials Engineering, 2024
V. S. Gerdjikov, Nianhua Li, V. B. Matveev, A. O. Smirnov, “On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems”, Theoret. and Math. Phys., 213:1 (2022), 1331–1347
Wu D., “The Direct Scattering Problem For Perturbed Kadomtsev-Petviashvili Multi Line Solitons”, J. Math. Phys., 62:9 (2021), 091513
Gerdjikov V.S., Smirnov A.O., Matveev V.B., “From Generalized Fourier Transforms to Spectral Curves For the Manakov Hierarchy. i. Generalized Fourier Transforms”, Eur. Phys. J. Plus, 135:8 (2020), 659
Wu D., “The Direct Scattering Problem For the Perturbed Gr(1,2)(> 0)Kadomtsev-Petviash-Vili II Solitons”, Nonlinearity, 33:12 (2020), 6729–6759
Biondini G., Hoefer M.A., Moro A., “Integrability, Exact Reductions and Special Solutions of the Kp-Whitham Equations”, Nonlinearity, 33:8 (2020), 4114–4132
Shai Horowitz, Yair Zarmi, “Kadomtsev–Petviashvili II equation: Structure of asymptotic soliton webs”, Physica D: Nonlinear Phenomena, 300 (2015), 1
Zarmi Ya., “Vertex Dynamics in Multi-Soliton Solutions of Kadomtsev-Petviashvili II Equation”, Nonlinearity, 27:6 (2014), 1499–1523
Zarmi Ya., “Nonlinear Quantum-Dynamical System Based on the Kadomtsev-Petviashvili II Equation”, J. Math. Phys., 54:6 (2013), 063515
V. S. Gerdjikov, “Two-dimensional Toda field equations related to the exceptional algebra $\mathfrak g_2$ : Spectral properties of the Lax operators”, Theoret. and Math. Phys., 172:2 (2012), 1085–1096
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
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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