Nonl2000

Nonlinearity 13 (2000) 837-848. Printed in the UK

Inelastic three-soliton collisions in a weakly discrete sine-Gordon system

A E Miroshnichenko^*, S V Dmitriev^**, A A Vasiliev^* and Т Shigenari^**

*) Department of Mathematical Modelling, Tver State University, 33 Zhelyabov St, 170000, Tver, Russia

^{**) Department of Applied Physics and Chemistry, University of Electro-Communications, Chofu-shi, Tokyo 182-8585, Japan
Abstract. The three-soliton solutions to the sine-Gordon equation describing the collision of a kink with a breather or with a kink-antikink pair are given and several separatrix three-soliton solutions are extracted from these solutions. The influence of a small perturbation on the three-soliton collisions is studied numerically. As the perturbed system the Frenkel-Kontorova model with a small degree of discreteness is considered. We show that in the three-soliton collisions, in the presence of small perturbation, energy exchange between solitons can take place. The degree of inelasticity of a three-soliton collision is extremely sensitive to the parameters of the collision.
AMS classification scheme numbers: 35Q51, 35Q53}