Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 017, 22 pages      arXiv:1002.1932      https://doi.org/10.3842/SIGMA.2010.017
Contribution to the Proceedings of the Eighth International Conference Symmetry in Nonlinear Mathematical Physics

Solitary Waves in Massive Nonlinear SN-Sigma Models

Alberto Alonso Izquierdo a, Miguel Ángel González León a and Marina de la Torre Mayado b
a) Departamento de Matemática Aplicada, Universidad de Salamanca, Spain
b) Departamento de Física Fundamental, Universidad de Salamanca, Spain

Received December 07, 2009; Published online February 09, 2010

Abstract
The solitary waves of massive (1+1)-dimensional nonlinear SN-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.

Key words: solitary waves; nonlinear sigma models.

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