Influence of dislocations on kink solutions of the double sine-Gordon equation

Dependences related to the formation of kinks and their interaction with local perturbations defined as a smooth function of coordinates multiplying the sine of complete argument in the double sine-Gordon equation are studied. It is shown that there are nonstationary kink solutions remaining within the perturbation domain. These solutions consist of two separate $2\pi$-kinks oscillating about the center of the perturbation. The interactions of these kinks with $4\pi$-kinks have a complicated character depending not only on the velocity but also on the phases of the kink pairs. The transmission, capture, and reflection of kinks are investigated. The computations were based on the quasispectral Fourier method and the fourth-order Runge–Kutta method.