Quantitative collective-coordinate description for Christ–Lee kink–antikink collisions

Develop a quantitative collective-coordinate method for kink–antikink collisions in the Christ–Lee model that can reproduce and explain the emergence of the observed fractal structure in the dependence of the outgoing velocity V_out on the parameter ε.

Background

In exploring how ε affects collision dynamics, the authors identify a novel fractal structure in V_out versus ε. They suggest a qualitative mechanism involving ε-dependent energy exchange between translational and shape modes within a collective-coordinate framework.

However, they explicitly state that they currently lack a quantitative collective-coordinate description for the Christ–Lee model sufficient to account for this phenomenon, highlighting an unresolved methodological gap.