Abstract:
The leading term in the t→∞ asymptotic behavior of the solution of the Cauchy problem for the Landau–Lifshitz equation is constructed in the case of “rapidly decreasing” initial data. The interaction of the oscillator background due to the continuum with soliton excitations is
described.
Citation:
R. F. Bikbaev, “Asymptotic behavior as t→∞ of the solution to the Cauchy problem for the Landau–Lifshitz equation”, TMF, 77:2 (1988), 163–170; Theoret. and Math. Phys., 77:2 (1988), 1117–1226
\Bibitem{Bik88}
\by R.~F.~Bikbaev
\paper Asymptotic behavior as $t\to\infty$ of the solution to the Cauchy problem for the Landau--Lifshitz equation
\jour TMF
\yr 1988
\vol 77
\issue 2
\pages 163--170
\mathnet{http://mi.mathnet.ru/tmf5944}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=978185}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 77
\issue 2
\pages 1117--1226
\crossref{https://doi.org/10.1007/BF01016377}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988AD07000001}
Linking options:
https://www.mathnet.ru/eng/tmf5944
https://www.mathnet.ru/eng/tmf/v77/i2/p163
This publication is cited in the following 14 articles:
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Yiling Yang, Engui Fan, “Soliton resolution and large time behavior of solutions to the Cauchy problem for the Novikov equation with a nonzero background”, Advances in Mathematics, 426 (2023), 109088
Yiling Yang, Engui Fan, “On the long-time asymptotics of the modified Camassa-Holm equation in space-time solitonic regions”, Advances in Mathematics, 402 (2022), 108340
Yiling Yang, Engui Fan, “Long-time Asymptotic Behavior for the Derivative Schrödinger Equation with Finite Density Type Initial Data”, Chin. Ann. Math. Ser. B, 43:6 (2022), 893
Yiling Yang, Engui Fan, “Soliton resolution for the short-pulse equation”, Journal of Differential Equations, 280 (2021), 644
Jian Xu, Engui Fan, “Long-time asymptotics for the Fokas–Lenells equation with decaying initial value problem: Without solitons”, Journal of Differential Equations, 259:3 (2015), 1098
A. V. Kitaev, A. H. Vartanian, “Asymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Nonvanishing Continuous Background”, SIAM J. Math. Anal., 30:4 (1999), 787
A V Kitaev, A H Vartanian, “Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector”, Inverse Problems, 13:5 (1997), 1311
A. I. Bobenko, A. M. Il'in, S. Yu. Dobrokhotov, A. R. Its, L. A. Kalyakin, V. B. Matveev, V. Yu. Novokshenov, A. B. Shabat, “Ramil' Faritovich Bikbaev (obituary)”, Russian Math. Surveys, 51:1 (1996), 129–133
R. F. Bikbaev, ““Domain walls” in the isotropic Heisenberg model”, Theoret. and Math. Phys., 95:1 (1993), 429–431
M Svendsen, H C Fogedby, “Phase shift analysis of the Landau-Lifshitz equation”, J. Phys. A: Math. Gen., 26:7 (1993), 1717
V. P. Kotlyarov, “Influence of a double continuous spectrum of the Dirac operator on the asymptotic solitons of a nonlinear Schrödinger equation”, Math. Notes, 49:2 (1991), 172–180
R. F. Bikbaev, “Distribution of magnetization in an easy-plane ferromagnet”, Theoret. and Math. Phys., 80:3 (1989), 1004–1006
R. F. Bikbaev, “Large-time asymptotics of the solution of the nonlinear Schrödinger equation with boundary conditions of step type”, Theoret. and Math. Phys., 81:1 (1989), 1011–1017
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