Abstract:
Explicit expressions that describe the leading term in the asymptotic
behavior of the solution of the Cauchy problem for the completely
anisotropic Landau–Lifshitz equation in the solitonless sector are obtained. The employed method is based on direct asymptotic analysis
of the corresponding matrix Riemann problem on a torus.
Citation:
R. F. Bikbaev, A. R. Its, “Asymptotics at t→∞ of the solution of the Cauchy problem for the Landau–Lifshitz equation”, TMF, 76:1 (1988), 3–17; Theoret. and Math. Phys., 76:1 (1988), 665–675
\Bibitem{BikIts88}
\by R.~F.~Bikbaev, A.~R.~Its
\paper Asymptotics at~$t\to\infty$ of the solution of the Cauchy problem for the Landau--Lifshitz equation
\jour TMF
\yr 1988
\vol 76
\issue 1
\pages 3--17
\mathnet{http://mi.mathnet.ru/tmf4977}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=961945}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 76
\issue 1
\pages 665--675
\crossref{https://doi.org/10.1007/BF01029424}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988U173100001}
Linking options:
https://www.mathnet.ru/eng/tmf4977
https://www.mathnet.ru/eng/tmf/v76/i1/p3
This publication is cited in the following 7 articles:
Harini Desiraju, Alexander Its, Andrei Prokhorov, “Nonlinear steepest descent on a torus: a case study of the Landau–Lifshitz equation”, Nonlinearity, 38:4 (2025), 045023
Harini Desiraju, Tomas Lasic Latimer, Pieter Roffelsen, “On a Class of Elliptic Orthogonal Polynomials and their Integrability”, Constr Approx, 2024
V. V. Kiselev, S. Batalov, “Relaxing solitons of a biaxial ferromagnet”, Theoret. and Math. Phys., 210:1 (2022), 46–67
Yuri Zhuravlev, Eduard Naichuk, Nikolai Iorgov, Oleksandr Gamayun, “Large-time and long-distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas”, Phys. Rev. B, 105:8 (2022)
Harini Desiraju, “Painlevé/CFT correspondence on a torus”, Journal of Mathematical Physics, 63:8 (2022)
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, “Asymptotic behavior as $t\to\infty$ of the solution to the Cauchy problem for the Landau–Lifshitz equation”, Theoret. and Math. Phys., 77:2 (1988), 1117–1226
Citation in format AMSBIB
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