Compact shell solitons in K field theories

TL;DR

This paper introduces new compact shell solitons in K field theories, providing exact analytical solutions in higher dimensions, classified as topological maps, and discusses their integrability and potential non-topological counterparts.

Contribution

The paper presents novel compact shell soliton solutions in K field theories with exact analytical forms and explores their topological classification and integrability properties.

Findings

Exact shell soliton solutions in 3+1 and 4+1 dimensions.

Solutions classified as maps $S^3 o S^3$ and suspended Hopf maps.

Existence of infinitely many exact shell solitons explained via generalized integrability.

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 $S^3 \to S^3$ 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. Finally, similar models allowing for non-topological compactons of the ball type in 3+1 dimensions are briefly discussed.