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Solitary waves in massive nonlinear \(\mathbb S^N\)-sigma models. (English) Zbl 1190.35191

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.

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
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