V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions of two-dimensional integrable equations using the $\bar\partial$-dressing method”, TMF, 167:3 (2011), 377–393; Theoret. and Math. Phys., 167:3 (2011), 725

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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 3, Pages 377–393
DOI: https://doi.org/10.4213/tmf6648 (Mi tmf6648)

This article is cited in 11 scientific papers (total in 11 papers)

New exact solutions of two-dimensional integrable equations using the

\bar{\partial}

$\bar\partial$ -dressing method

V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev

Novosibirsk State Technical University, Novosibirsk, Russia

Full-text PDF (467 kB) Citations (11)

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DOI: https://doi.org/10.4213/tmf6648

Abstract: We review new classes of exact solutions with functional parameters with constant asymptotic values at infinity of the Nizhnik–Veselov–Novikov equation and new classes of exact solutions with functional parameters of two-dimensional generalizations of the Kaup–Kupershmidt and Sawada–Kotera equations, constructed using the Zakharov–Manakov

\bar{\partial}

$\bar\partial$ -dressing method. We present subclasses of multisoliton and periodic solutions of these equations and give examples of linear superpositions of exact solutions of the Nizhnik–Veselov–Novikov equation.

Keywords: Nizhnik–Veselov–Novikov equation, two-dimensional Kaup–Kupershmidt equation, two-dimensional Sawada–Kotera equation, solutions with functional parameters, two-dimensional stationary Schrödinger equation, soliton, transparent potential.

Received: 23.06.2011

English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 3, Pages 725–739
DOI: https://doi.org/10.1007/s11232-011-0057-3

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “New exact solutions of two-dimensional integrable equations using the

\bar{\partial}

$\bar\partial$ -dressing method”, TMF, 167:3 (2011), 377–393; Theoret. and Math. Phys., 167:3 (2011), 725–739

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf6648

https://doi.org/10.4213/tmf6648

https://www.mathnet.ru/eng/tmf/v167/i3/p377

This publication is cited in the following 11 articles:

Chenyang Yao, Junyi Zhu, Xueru Wang, “Relative voltage and current for the self-dual network equation characterized by Dbar data”, Physics Letters A, 499 (2024), 129359
Chanyuan Wang, Raghda A. M. Attia, Suleman H. Alfalqi, Jameel F. Alzaidi, Mostafa M. A. Khater, “Stability analysis and conserved quantities of analytic nonlinear wave solutions in multi-dimensional fractional systems”, Mod. Phys. Lett. B, 2024
Mostafa M.A. Khater, “Pfaffian solutions and nonlinear dynamics of surface waves in two horizontal and one vertical directions with dispersion, dissipation and nonlinearity effects”, Alexandria Engineering Journal, 108 (2024), 232
Yadi Xu, Junyi Zhu, “A new coupled differential–difference KP type system”, Chaos, Solitons & Fractals, 167 (2023), 113107
Tengfei Liu, “A 2+1 dimensional Volterra type system with nonzero boundary conditions via Dbar dressing method”, Nonlinear Dyn, 111:1 (2023), 671
Chang J.-H., “The interactions of solitons in the Novikov–Veselov equation”, Appl. Anal., 95:6 (2016), 1370–1388
Adem A.R., Lu X., “Travelling wave solutions of a two-dimensional generalized Sawada–Kotera equation”, Nonlinear Dyn., 84:2 (2016), 915–922
V. G. Dubrovsky, A. V. Topovsky, M. Yu. Basalaev, “Solutions with Functional Parameters of 2+1-Dimensional Integrable Nonlinear Equations. Two Dimensional Integrable Generalization of the Kaup–Kupershmidt Equation”, Russ Phys J, 58:7 (2015), 930
Dubrovsky V.G., Topovsky A.V., “About Linear Superpositions of Special Exact Solutions of Nizhnik-Veselov-Novikov Equation”, Physics and Mathematics of Nonlinear Phenomena 2013, Journal of Physics Conference Series, 482, IOP Publishing Ltd, 2014, 012011
Dubrovsky V.G., Topovsky A.V., “About Simple Nonlinear and Linear Superpositions of Special Exact Solutions of Veselov-Novikov Equation”, J. Math. Phys., 54:3 (2013), 033509
Adem A.R., Khalique Ch.M., “Exact Solutions and Conservation Laws of a Two-Dimensional Integrable Generalization of the Kaup-Kupershmidt Equation”, J. Appl. Math., 2013, 647313

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

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