Narrow Results

A nonassociative generalization of the principal fiber bundles with a smooth loop mapping on the fiber is presented. Our approach allows us to construct a new kind of gauge theories that involve higher "nonassociative" symmetries.

A physical model of the O(3)-invariant coupled integrable dispersionless equations that describe the dynamics of a focused system within the background of a plane gravitational field is studied. The investigation is carried out both numerically and analytically, and is pursued both in the Lie algebra and quasigroup theory contexts in which the structure constants of the former are extended into the structure functions of the latter. The energy density and topological structures such as loop solitons are examined.