Abstract
For the model of the two-dimensional stationary Heisenberg magnet, real finite-gap solutions that describe the main structures that are almost periodic with respect tox andy are constructed. Some solutions of boundary-value problems are considered.
Similar content being viewed by others
References
L. D. Landau and E. M. Lifshitz, in:Collected Works of L. D. Landau, Vol. 1 [in Russian], Nauka, Moscow (1969), p. 128.
R. F. Bikbaev, A. I. Bobenko, and A. R. Its, “The Landau—Lifshitz equation. Theory of exact solutions,” Preprint DonFTI-84-6, 7(81-82), Parts I and II [in Russian], Physicotechnical Institute, Donetsk (1984).
A. V. Mikhailov, “Integrable magnetic models,” in:Solitons (eds. V. Zakharov, V. Pokrovski and Trullinger), North-Holland, Amsterdam (1986).
R. F. Bikbaev,Mat. Zametki,48, 10 (1990).
A. A. Belavin and A. M. Polyakov,Pis'ma Zh. Eksp. Teor. Fiz.,22, 503 (1975).
R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris,Solitons and Nonlinear Wave Equations, Academic Press, New York (1983).
A. I. Bobenko,Zap. Nauchn. Semin. LOMI,179, 32 (1989).
R. F. Bikbaev and V. O. Tarasov,Algebra i Analiz,3, 78 (1991).
Additional information
St Petersburg Branch, V. A. Steklov Mathematics Institute, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 165–172, January, 1993.
Rights and permissions
About this article
Cite this article
Bikbaev, R.F. Finite-gap solutions of two-dimensional isotropic ferromagnet with fixed boundary conditions. Theor Math Phys 94, 117–122 (1993). https://doi.org/10.1007/BF01017003
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01017003