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 
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/
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     author = {S. P. Popov},
     title = {Interactions of breathers and kink pairs of the double {sine-Gordon} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1954--1964},
     year = {2014},
     volume = {54},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_12_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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