Kink Dynamics and the Third Integral of Motion in the Double Sine-Gordon Equation
It is shown that in certain asymptotic space-time region the dynamics of the double sine-Gordon (DSG) kinks are described by the Toda lattice (TL) equation. A candidate for the third integral of motion to the DSG equation is proposed with the help of integrability of the TL equation. The time dependence of the proposed integral of motion is numerically studied for the kink-kink and kink-antikink collisions and is related to whether trajectories in phase space are regular or chaotic.
富山県立大学紀要 4, 112-129, 1994-03