I. A. Anders, V. P. Kotlyarov, E. Ya. Khruslov, “Curved asymptotic solitons of the Kadomtsev–Petviashvili equation”, TMF, 99:1 (1994), 27–35; Theoret. and Math. Phys., 99:1 (1994), 402

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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 99, Number 1, Pages 27–35 (Mi tmf1564)

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

Curved asymptotic solitons of the Kadomtsev–Petviashvili equation

I. A. Anders, V. P. Kotlyarov, E. Ya. Khruslov

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine

Full-text PDF (771 kB) Citations (16)

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Abstract: We prove the existence of solutions of the Kadomtsev–Petviashvili equation whose temporal asymptotics can be represented as a superposition of curved solitons.

Received: 05.01.1993

English version:
Theoretical and Mathematical Physics, 1994, Volume 99, Issue 1, Pages 402–408
DOI: https://doi.org/10.1007/BF01018794

Bibliographic databases:

Language: Russian

Citation: I. A. Anders, V. P. Kotlyarov, E. Ya. Khruslov, “Curved asymptotic solitons of the Kadomtsev–Petviashvili equation”, TMF, 99:1 (1994), 27–35; Theoret. and Math. Phys., 99:1 (1994), 402–408

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

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Linking options:

https://www.mathnet.ru/eng/tmf1564

https://www.mathnet.ru/eng/tmf/v99/i1/p27

This publication is cited in the following 16 articles:

Santucci F., Santini P.M., “On the dispersionless Kadomtsev–Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks”, J. Phys. A-Math. Theor., 49:40 (2016), 405203
V. Kotlyarov, A. Minakov, “Step-initial function to the mKdV equation: hyper-elliptic long-time asymptotics of the solution”, Zhurn. matem. fiz., anal., geom., 8:1 (2012), 38–62
A. Minakov, “Asymptotics of rarefaction wave solution to the mKdV equation”, Zhurn. matem. fiz., anal., geom., 7:1 (2011), 59–86
Minakov A., “Long-time behavior of the solution to the mKdV equation with step-like initial data”, J. Phys. A: Math. Theor., 44:8 (2011), 085206
Kotlyarov V., Minakov A., “Riemann–Hilbert problem to the modified Korteveg-de Vries equation: Long-time dynamics of the steplike initial data”, J Math Phys, 51:9 (2010), 093506
Zhi-fang Li, Hang-yu Ruan, “(2+1)-dimensional Davey–Stewartson I description in a 2D lattice model”, Phys. Scr., 77:6 (2008), 065009
O. M. Kiselev, “Higher-dimensional nonlinear integrable equations: asymptotics of solutions and perturbations”, J Math Sci, 125:5 (2005), 689
O. M. Kiselev, “Higher-dimensional nonlinear integrable equations: Asymptotics of solutions and perturbations”, J Math Sci, 125:5 (2005), 689
O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230
de Monvel, AB, “Soliton asymptotics of rear part of non-localized solutions of the Kadomtsev-Petviashvili equation”, Journal of Nonlinear Mathematical Physics, 9:1 (2002), 58
Anders, I, “Soliton asymptotics of nondecaying solutions of the modified Kadomtsev-Petviashvili-I equation”, Journal of Mathematical Physics, 42:8 (2001), 3673
Igor Anders, “Asymptotics of coupled solutions of the Kadomtsev–Petviashvili equation”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 333:9 (2001), 891
Anders, I, “Asymptotic solitons of the Johnson equation”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 284
Nils Svanstedt, “Correctors for the Homogenization of Monotone Parabolic Operators”, JNMP, 7:3 (2000), 268
I.A. Anders, E.Ya. Khruslov, V.P. Kotlyarov, “Soliton asymptotics of non-localized solutions of non-linear evolutionary equations”, Nonlinear Analysis: Theory, Methods & Applications, 30:7 (1997), 3951
D. Yu. Ostapenko, A. P. Pal-Val, E. Ya. Khruslov, “Uniform asymptotic formulas for the curved solitons of the Kadomtsev–Petviashvili equations”, Theoret. and Math. Phys., 108:2 (1996), 1013–1018

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

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