Solitary Waves in Massive Nonlinear S^N-Sigma Models

TL;DR

This paper explores solitary wave solutions in massive nonlinear S^N-sigma models, linking them to separatrix trajectories and analyzing their stability through spectral methods and Morse index theorem.

Contribution

It establishes a correspondence between solitary waves and separatrix trajectories, and analyzes the stability of various kink solutions in these models.

Findings

Topological and non-topological kinks identified.

Stability of embedded sine-Gordon kinks analyzed.

Instability of some kinks demonstrated using Morse index theorem.

Abstract

The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional Neumann mechanical problem. There are topological (heteroclinic trajectories) and non-topological (homoclinic trajectories) kinks. The stability of some embedded sine-Gordon kinks is discussed by means of the direct estimation of the spectra of the second-order fluctuation operators around them, whereas the instability of other topological and non-topological kinks is established applying the Morse index theorem.