Compact shell solitons in K field theories
Abstract
Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological solitons, and may be classified as maps S3 S3 and suspended Hopf maps, respectively. The Lagrangian of these models is given by a scalar field with a non-standard kinetic term (K field) coupled to a pure Skyrme term restricted to S2, rised to the appropriate power to avoid the Derrick scaling argument. Further, the existence of infinitely many exact shell solitons is explained using the generalized integrability approach. Finally, similar models allowing for non-topological compactons of the ball type in 3+1 dimensions are briefly discussed.