This article is cited in 7 papers

ANALYSIS AND MODELING OF COMPLEX LIVING SYSTEMS

Control of the dynamics of the kink of the modified sine-Gordon equation by the external exposure with varying parameters

F. K. Zakir'yanov^a, L. V. Yakushevich<sup>b

a</sup> Bashkir State University, 32 Z. Validi str., Ufa, 450074, Russia
^b Institute of Cell Biophysics, 3 Institutskaya str., Pushchino, 142290, Russia

Abstract: The paper presents results that confirm the ability to control the movement of the kink of the modified sine-Gordon equation with variable external force parameters. Three types of external influences have been considered: permanent action, periodic action with a constant frequency and a frequency-modulated periodic exposure. The dependences of the position and velocity of the kink on time for various values of the parameters of external influence were obtained using the method of McLaughlin and Scott. It is shown that by changing the settings, one can adjust the velocity and direction of movement of the kink.

Keywords: sine-Gordon equation, soliton, kink, control of the movement of the kink, nonlinear DNA dynamics.

UDC: 530.182.1

Received: 29.06.2013
Revised: 22.11.2013

DOI: 10.20537/2076-7633-2013-5-5-821-834