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TMF, 1994, Volume 99, Number 1, Pages 27–35 (Mi tmf1564)  

This article is cited in 10 scientific papers (total in 10 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

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

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English version:
Theoretical and Mathematical Physics, 1994, 99:1, 402–408

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Received: 05.01.1993

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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\by I.~A.~Anders, V.~P.~Kotlyarov, E.~Ya.~Khruslov
\paper Curved asymptotic solitons of the Kadomtsev--Petviashvili equation
\jour TMF
\yr 1994
\vol 99
\issue 1
\pages 27--35
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1302457}
\zmath{https://zbmath.org/?q=an:0850.35093}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 99
\issue 1
\pages 402--408
\crossref{https://doi.org/10.1007/BF01018794}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Anders, I, “Asymptotic solitons of the Johnson equation”, Journal of Nonlinear Mathematical Physics, 7:3 (2000), 284  crossref  mathscinet  zmath  adsnasa  isi
    3. Anders, I, “Soliton asymptotics of nondecaying solutions of the modified Kadomtsev-Petviashvili-I equation”, Journal of Mathematical Physics, 42:8 (2001), 3673  crossref  mathscinet  zmath  adsnasa  isi
    4. 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  crossref  mathscinet  zmath  adsnasa  isi
    5. O. M. Kiselev, “Asymptotics of solutions of higher-dimensional integrable equations and their perturbations”, Journal of Mathematical Sciences, 138:6 (2006), 6067–6230  mathnet  crossref  mathscinet  zmath  elib
    6. 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  crossref  isi
    7. A. Minakov, “Asymptotics of rarefaction wave solution to the mKdV equation”, Zhurn. matem. fiz., anal., geom., 7:1 (2011), 59–86  mathnet  mathscinet  zmath  elib
    8. 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  crossref  isi
    9. 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  mathnet  mathscinet  zmath
    10. 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  crossref  mathscinet  zmath  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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