Compact shell solitons in K field theories

Understand

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 $S^3 \to S^3$ 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 $S^2$, 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.