Chaotic solitons in the sine-Gordon model with periodic potential

Static solitons in one-dimensional scalar field theory obey the same equations as a particle in multidimensional classical mechanics. One can expect that the structure of such solitons differs significantly if there is dynamic chaos in the corresponding mechanical system. This can happen both in models of several scalar fields and in models with a potential that is clearly inhomogeneous in space. In particular, I will consider the sine-Gordon model in the external "Dirac lattice" potential. In such a system, the number of different solitons increases exponentially with increasing length, and the rate of this exponential growth is related to the topological entropy of a similar mechanical system. Moreover, I will show that the values of the field of stable solitons form a fractal and estimate its dimension. Finally, I will show how the distribution of points in this fractal is related to the Kolmogorov-Sinai entropy of a mechanical system – another important quantity characterizing chaos. The report is based on [1].

References

1. D.G. Levkov, V.E. Maslov, E.Y. Nugaev, Chaos, Solitons & Fractals, 139 (2020), 110079, arXiv: 2004.13052