Solitary waves in massive non-linear S²-sigma and S³-sigma models

Abstract:
In this talk we present the kink solitary waves of two massive nonlinear sigma models, with respectively the spheres S² and S³ as target manifolds. Using the mechanical analogy, kinks are finally showed to be equivalent to the separatrix solutions of the Neumann mechanical problem with repulsive force. The stability of the topological kinks is discussed by means of a direct estimation of the spectra of the second-order fluctuation operators around the kinks, whereas the lack of stability of the non-topological kinks is unveiled by application of the Morse Index Theorem.

Presentation