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Matematicheskaya Fizika, Analiz, Geometriya [Mathematical Physics, Analysis, Geometry], 2002, Volume 9, Number 2, Pages 272–280
(Mi jmag291)
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This article is cited in 1 scientific paper (total in 1 paper)
Perturbation of soliton for Davey–Stewartson II equation
R. R. Gadyl'shina, O. M. Kiselevb a Department of Physics and Mathematics, Bashkir State Pedagogic University, 3-a Oktyabr'skoi revolyucii Str., Ufa, 450000, Russia
b Institute of Mathematics of Ufa Sci. Centre of RAS, 112 Chernyshevsky Str., Ufa, 450077, Russia
Abstract:
It is known that, under a small perturbation (of order $\varepsilon$) of lump (soliton) for Davey–Stewartson (DS-II) equation, the scattering data become nonsoliton. As a result, the solution has the form of Fourier type integral. Asymptotical analysis, given in this work, shows that in spite of dispersion, the main term of the asymptotic expansion for the solution has the solitary wave form up to large time (of order $\varepsilon^{-1}$).
Received: 26.11.2001
Citation:
R. R. Gadyl'shin, O. M. Kiselev, “Perturbation of soliton for Davey–Stewartson II equation”, Mat. Fiz. Anal. Geom., 9:2 (2002), 272–280
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https://www.mathnet.ru/eng/jmag291 https://www.mathnet.ru/eng/jmag/v9/i2/p272
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