Three-Soliton Solutions

Standing Kink and Moving Breather collision

[Maple Plot]

Standing Breather and Moving Kink collision

[Maple Plot]

In the two last figures, the kink-breather collisions are presented for the cases when one of the quasiparticles moves and another one is at rest. Of course, for these collisions the total charge [Maple Math] = [Maple Math] , is also conserved. These two solutions, describing kink-breather collisions, are actually identical in the sense that one of them can be transformed to another by means of the Lorentz transformation for an inertial system. All the collisions described above are the elastic collisions or, in other words, there is no energy and momentum exchange between colliding quasiparticles. However, for the discrete sine-Gordon system the collision of more than two solitons can be strongly inelastic even at a very small degree of discreteness. For example, in Ref. [2], the domain of parameters has been given where the transformation of kink-breather solution to the kink-antikink-kink solution becomes possible. This transformation is not forbidden by the charge conservation law because [Maple Math] = [Maple Math] .