and Computational Methods

doi: 10.18698/2309-3684-2016-4-316

The study examined the formation and evolution of stationary and moving breathers of a two-dimensional O(3) nonlinear sigma model. We detected analytical form of trial functions of two-dimensional sine-Gordon equations, which over time evolve into periodic (breather) solutions. According to the solutions found, by adding the rotation to an A3-field vector in isotopic space S^2 we obtained the solutions for the O(3) nonlinear sigma model. Furthermore, we conducted the numerical study of the solutions dynamics and showed their stability in a stationary and a moving state for quite a long time, although in the presence of a weak radiation.

[1] Minzoni A.A., Smyth N.F., Worthy A.L. Evolution of two-dimensional standing and travelling breather solutions for the sine-Gordon equation. Phys. D, 2004, no. 189, pp. 167-187.

[2] Xin J.X. Modeling light bullets with the two-dimensional sine-Gordon equation. Phys. D, 2000, no.135, pp. 345-368.

[3] Piette B., Zakrjewsky W.J. Metastable stationary solutions of the radial D-dimensional sine-Gordon model. Nonlinearity, 1998, no. 11, pp. 1103-1110.

[4] Smyth N.F., Worthy A.L. Soliton evolution and radiation loss for the Sine-Gordon equation. Phys. Rev. E, 1999, no. 60, pp. 2330-2336.

[5] Minzoni A.A., Smyth N.F., Worthy A.L. Pulse evolution for a two-dimensional Sine-Gordon equation. Phys. D, 2001, no. 159, pp. 101-123.

[6] Malomed B.A. Decay of shrinking solitons in multidimensional sine-Gordon equation. Physica 24D, 1987, pp. 155-171.

[7] Christiansen P.L., Malomed B.A. Oscillations of Eccentric Pulsons. Physica Scripta, 1997, vol. 55, pp. 131-134.

[8] Geicke J. Cylindrical Pulsons in Nonlinear Relativistic Wave Equations. Physica Scripta, 1984, vol. 29, pp. 431-434.

[9] Muminov Kh.Kh., Chistyakov D.Yu. Doklady Akademii nauk Respubliki Tadzhikistan – Reports of Academy of Sciences of the Republic of Tajikistan, 2004, vol. 47, no. 9-10, pp. 45-50.

[10] Muminov Kh.Kh., Shokirov F.Sh. Doklady Akademii nauk Respubliki Tadzhikistan – Reports of Academy of Sciences of the Republic of Tajikistan, 2011, vol. 54, no. 10, pp. 825-830.

[11] Muminov Kh.Kh., Shokirov F.Sh. Dynamics of two-dimensional breathers in O(3) vectorial nonlinear sigma-model. The Book of abstracts of the International Conference Mathematical modeling and computational physics. Russia, Dubna, 2013, p.134.

[12] Muminov Kh.Kh., Shokirov F.Sh. LI Vserossiskaia konferentsiia po problemam dinamiki, fiziki chastits, fiziki plazmy i optoelektroniki – Proceedings of LI-Russian conference on the problems of dynamics, particle physics, plasma physics and optoelectronics. Moscow: Publishing House of Peoples' Friendship University, 2015, pp. 94-98.

[13] Samarsky A.A. Teoriia raznostnykh skhem [The theory of difference schemes]. Moscow, Nauka, 1977, 657 p.

[14] Samarsky A.A., Vabishevich P. N., Gulin A.V. Stability of operator-difference schemes. Differ. Equ., vol. 35, no. 2, 1999, pp. 151-186.

[15] Muminov Kh.Kh. Doklady Akademii nauk Respubliki Tadzhikistan – Reports of Academy of Sciences of the Republic of Tajikistan, 2002, vol. 45, no. 10, pp. 21-27.

[16] Muminov Kh.Kh. Doklady Akademii nauk Respubliki Tadzhikistan – Reports of Academy of Sciences of the Republic of Tajikistan, 2002, vol. 45, no.10, pp. 28-36.

[17] Shokirov F.Sh. Stationary and moving breathers in (2+1)-dimensional O(3) nonlinear σ-model. – arXiv:1605.01000 [nlin.PS], 2016, 11 p.

[18] Mahankov V.G. Solitony i chislennyi eksperiment – Solitons and numerical experiment. Particles & Nuclei, 1983, vol.14, no. 1, pp. 123-180.

Shokirov F. Mathematical modeling of breathers of two-dimensional O(3) nonlinear sigma model. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 3-16

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