Effect of discreteness on a sine-Gordon three-soliton solution

S.V. Dmitriev^a, T. Shigenari^a, A.A. Vasiliev^b, A.E. Miroshnichenko^b

a Department of Applied Physics and Chemistry, University of Electro-Communications, Chofu-shi, Tokyo 182, Japan

^{b Department of Mathematical Modeling, Tver State University, 33 Zhelyabov Street, 170000 Tver, Russia}

Received 23 February 1998; revised manuscript received 18 May 1998; accepted for publication 4 June 1998

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Abstract

The collision between a kink and a high amplitude breather in the Frenkel-Kontorova chain with a small degree of discreteness was studied numerically and the results were compared with an exact three-soliton solution to the sine-Gordon (SG) equation. It was found that there exists a narrow range of parameters of quasiparticles where the collision in the discrete system is strongly inelastic and that the inelastic collision occurs in the vicinity of a separatrix of the SG three-soliton solution.

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Keywords: Sine-Gordon equation; Many-soliton solution; Frenkel-Kontorova chain; Discreteness effect; Stochastic instability; Inelastic collision