Geodesic
Interactions of breathers and kink pairs of the double sine-Gordon equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 12, pp. 1954-1964 Cet article a éte moissonné depuis la source Math-Net.Ru

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The double sine-Gordon equation is considered in the case of a small parameter multiplying the half-angle sine. It is shown that initial distributions consisting of combinations of kink solutions to the sine-Gordon equation decompose into breathers, single kinks, and kink-kink (kink-anti-kink) long-lived pairs. The interactions of kink pairs with each other and with breathers in bifurcation modes characterized by considerable variations in the kink velocities, frequencies, and oscillation amplitudes are studied. The numerical simulation is based on the quasi-spectral Fourier method and the fourth-order Runge–Kutta method. 
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S. P. Popov. Interactions of breathers and kink pairs of the double sine-Gordon equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 12, pp. 1954-1964. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_12_a7/

[1] Makhankov V. G., “Solitony i chislennyi eksperiment”, Fizika elementarnykh chastits i atomnogo yadra, 14:1 (1983), 123–180

[2] Dos Santos C., Rubiera-Garcia D., “Generalized sine-Gordon solitons”, J. Phys. A: Math. Theor., 44:42 (2011), 425402–425419 | DOI

[3] Bordag M., Munos-Castaheda J. M., “Quantum vacuum interaction between two sine-Gordon kinks”, J. Phys. A: Math. Theor., 45:35 (2012), 374012–374026 | DOI

[4] Kalbermann G., “The sine-Gordon wobble”, J. Phys. A: Math. Gen., 37:48 (2004), 11603–11612 | DOI

[5] Belova T. I., Kudryavtsev A. E., “Solitony i ikh vzaimodeistviya v klassicheskoi teorii polya”, Uspekhi fiz. nauk, 167:4 (1997), 377–406 | DOI

[6] Ekomasov E. G., Gumerov A. M., “Kollektivnoe vliyanie primesei na dinamiku kinkov modifitsirovannogo uravneniya sinus-Gordona”, Kompyuternye issledovaniya i modelirovanie, 5:3 (2013), 403–412

[7] Gani V. A., Kudryavtsev A. E., “Kink-antikink interaction in the double sine-Gordon equation and the problem of resonance frequencies”, Phys. Rev. E, 60:3 (1999), 3305–3309 | DOI

[8] Popov S. P., “Vozmuschennye solitonnye resheniya uravneniya sin-Gordona”, Zh. vychisl. matem. i matem. fiz., 49:12 (2009), 2182–2188

[9] Peyravi M., Montakhab A., Riazi N., Gharaati A., “Interaction properties of the periodic and step-like solutions of the double-sine-Gordon equation”, Eur. Phys. J. B, 72 (2009), 269–277 | DOI

[10] Hu H. C., Lou S. Y., Chow K. W., “New interaction solutions of multiply periodic, quasi-periodic and non-periodic waves for the $(n+1)$-dimensional double sine-Gordon equations”, Chaos, Solitons and Fractals, 31 (2007), 1213–1222 | DOI