Solitons in complex systems of chiral fields with Kuramoto interactions.

摘要: We construct a complex system of N chiral fields, each regarded as node or constituent field-theoretic system, which interact by means chirally invariant potentials across network connections. In the classical case, these interactions are identical similar to Kuramoto interactions, leading synchronization phenomena for well-known model and its many extensions generalizations higher dimensions. consider systems arbitrary size N, where carries conserved charge topological origin, evolve according coupled second-order, Lorentz invariant, nonlinear partial differential equations. Stable soliton configurations occur consequence not necessarily from self-interactions fundamental fields. 1 + dimensions, models allow multi-soliton that = 2 determined sine-Gordon equation 3 reduce in special cases double equation, has exact double-kink static solutions consisting solitons positioned at locations. Planar three-dimensional networked skyrmions appear Such can be viewed general bound states exist together with usual excitations. Whereas first-order lead emergent such synchronization, same fields result rich variety states.