Abstract. Multibreathers and discrete solitons are among the most studied solutions in nonlinear Hamiltonian lattices, and they are of great relevance for those interested in coherent structures. These objects are often investigated in the so called anti-continuous limit; it is interesting, not only from the mathematical point of view, that in such a framework their continuation from the zero-coupling limit is naturally related to the classical problem of the breaking of resonant tori in nearly integrable Hamiltonian systems. We will discuss the existence and non existence of the above mentioned continuations in the particularly delicate case of degenerate solutions. We will consider some examples in one-dimensional dNLS and KG chains. We will review some techniques involved in the mathematical investigation, ranging from Lyapunov-Schmidt decomposition, constructive normal form schemes and Newton-Kantorovich fixed point method.
The results presented are joint with V. Danesi, P. Kevrekidis, V. Koukouloyannis, T. Penati and M. Sansottera.
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