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Interactions of breathers and kink pairs of the double sine-Gordon equation

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Abstract

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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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    S. P. Popov

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  1. S. P. Popov
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Correspondence to S. P. Popov.

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Original Russian Text © S.P. Popov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 12, pp. 1954–1964.

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Popov, S.P. Interactions of breathers and kink pairs of the double sine-Gordon equation. Comput. Math. and Math. Phys. 54, 1876–1885 (2014). https://doi.org/10.1134/S0965542514120112

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  • DOI: https://doi.org/10.1134/S0965542514120112

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