Coupled solitons in lattices
Vladimir Konotop, Madeira
The general theory of small amplitude envelope solitons in
one-dimentional lattices with cubic and quartic nonlinearities is
developed. It is shown that for large diversity
of both linear interactions among the particles and types of
nonlinearity the dynamics of chain exsitations is governed either by
the nonlinear Schrödinger equation or by the system of coupled
nonlinear Schrödinder equations. In particular, the theory allows
including lattices with long-range interactions and chains with a
complex cell in the unique scheme, which is
the envelope function approach. The novel classes of solitons in
diatomic lattices and in chains with long-range interactions are
described as particular examples.
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