Izquierdo, Alberto Alonso; León, Miguel Ángel González; De La Torre Mayado, Marina Solitary waves in massive nonlinear \(\mathbb S^N\)-sigma models. (English) Zbl 1190.35191 SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 017, 22 p. (2010). Summary: The solitary waves of massive \((1+1)\)-dimensional nonlinear \(\mathbb S^N\)-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. Cited in 1 Document MSC: 35Q51 Soliton equations 81T99 Quantum field theory; related classical field theories 35B35 Stability in context of PDEs 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems 37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems Keywords:solitary waves; nonlinear sigma models PDFBibTeX XMLCite \textit{A. A. Izquierdo} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 017, 22 p. (2010; Zbl 1190.35191) Full Text: DOI arXiv EuDML EMIS