Stationary Solitons in discrete NLS with non-nearest neighbour interactions

The aim of this paper is to provide a construction of stationary discrete solitons in an extended one-dimensional Discrete NLS model with non-nearest neighbour interactions. These models, models of the type with long-range interactions were studied in various other contexts. In particular, it was shown that, if the interaction strength decays sufficiently slowly as a function of distance, it gives rise to bistability of solitons, which may find applications in their controllable switching. Dynamical lattices with long-range interactions also serve as models for energy and charge transport in biological molecules. Using a dynamical systems method we are able to construct, with great accuracy, stationary discrete solitons for our model, for a large region of the parameter space.

💡 Research Summary

The paper investigates stationary (time‑independent) localized solutions—often called discrete solitons or breathers—in a one‑dimensional discrete nonlinear Schrödinger (DNLS) lattice that includes not only the usual nearest‑neighbour coupling but also a non‑nearest‑neighbour (next‑nearest) interaction term. The governing equation is

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