Bifurcations of travelling wave solutions in the discrete NLS equations

We study discrete nonlinear Schrödinger (NLS) equations, which include the cubic NLS lattice with on-site interactions and the integrable Ablowitz–Ladik lattice. Standing wave solutions are known to exist in the discrete NLS equations outside of the finite spectral band. We study travelling wave solutions which have nonlinear resonances with unbounded linear spectrum. By using center manifold and normal form reductions, we show that a …