Abstract
We use the dressing method to find exact solutions of the Landau-Lifshitz equation for a ferromagnet with light-axis anisotropy. These solutions describe the interaction of a nonlinear precession wave of arbitrary amplitude with solitons. We analyze the change of the internal structure and the physical parameters of the solitons as a result of their interaction with the magnetization wave. We find an infinite series of integrals of motion that stabilize the soliton on the background of the pumping wave.
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References
A.M. Kosevich, B. A. Ivanov, and A. S. Kovalev, Nonlinear Waves of Magnetization: Dynamical and Topological Solitons [in Russian], Naukova Dumka, Kiev (1983).
M. A. Shamsutdinov, I. Yu. Lomakina, and V. N. Nazarov, Ferro- and Antiferromagnetodynamics: Nonlinear Oscillations, Waves, and Solitons [in Russian], Gilem, Ufa (2007).
A. V. Mikhailov and A. I. Yaremchuk, JETP Lett., 39, 354–357 (1984).
A. I. Yaremchuk, Theor. Math. Phys., 62, 101–105 (1985).
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl., Plenum, New York (1984).
R. F. Bikbaev, A. I. Bobenko, and A. R. Its, “Landau-Lifshits equation: Theory of exact solutions II [in Russian],” Preprint, Don-FTI, Donetsk (1984).
R. F. Bikbaev, A. I. Bobenko, and A. R. Its, Sov. Math. Dokl., 28, 512–516 (1983).
A. Erdélyi, W. Magnus, F. Oberhettinger, and F. Tricomi, Higher Transcendental Functions, Vol. 3, McGraw-Hill, New York (1955).
A. E. Borovik, S. Klama, and S. I. Kulinch, Phys. D, 32, 107–134 (1988).
N. I. Akhiezer, Elements of the Theory of Elliptic Functions [in Russian], Nauka, Moscow (1970); English transl. (Transl. Math. Monogr., Vol. 79), Amer. Math. Soc., Providence, R. I. (1990).
A. V. Mikhailov, “Integrable magnetic models,” in: Solitons (Mod. Prob. Cond. Matter Sci., Vol. 17, S. E. Trullinger, V. E. Zakharov, and V. L. Pokrovsky, eds.), Elsevier, Amsterdam (1986), pp. 625–690.
Yu. L. Rodin, Phys. D, 11, 90–108 (1984).
A. B. Borisov and V. V. Kiselev, Theor. Math. Phys., 54, 160–167 (1983).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 163, No. 1, pp. 94–113, April, 2010.
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Kiselev, V.V., Raskovalov, A.A. Interaction of a breather with a magnetization wave in a ferromagnet with light-axis anisotropy. Theor Math Phys 163, 479–495 (2010). https://doi.org/10.1007/s11232-010-0037-z
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DOI: https://doi.org/10.1007/s11232-010-0037-z