Monday, October 19, 11:30am - 12:30pm (HH410)
Finite-range DNLS lattices, where interactions extend beyond nearest neighbours, support richer dispersion degeneracies than the classical model. This talk focuses on travelling waves near a zero-dispersion carrier, where a cubic degeneracy of the Fourier symbol generates a six-dimensional reversible centre manifold and a third-order amplitude equation. Identifying this equation with the classical Pelinovsky–Rothos normal form transfers known existence, non-existence, and persistence results for double-humped homoclinic orbits to arbitrary finite interaction range; direct numerical integration of the full lattice confirms the predicted O(ε^4) convergence. We close by briefly outlining a parallel construction for the associated stationary problem, where homoclinic standing waves are obtained variationally as limits of periodic constrained maximizers on an invariant cone of positive, unimodal profiles.