Symmetry in Nonlinear Mathematical Physics - 2009
Miguel Ángel González León and Marina de la Torre Mayado (Universidad de Salamanca, Spain)
Solitary waves in massive non-linear S2-sigma and S3-sigma models
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.