The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of Melnikov's perturbation method. The latter provides analytical conditions for the existence of such waves that bifurcate from the homogeneous nonlinear modes of the system and are located at specific positions with respect to the underlying potential. It is shown that the necessary conditions for the existence of continuous families of stationary solitary waves, as they arise from Melnikov theory, provide general constraints for the real and imaginary part of the potential, that are not restricted to symmetry conditions or specific types of potentials. Direct simulations are used to compare numerical results with the analytical predictions, as well as to investigate the propagation dynamics of the solitary waves.

No abstract

No abstract

No abstract

We examine the role of long-range interactions on the dynamical and statistical properties of two 1D lattices with on-site potentials that are known to support discrete breathers: the Klein-Gordon (KG) lattice which includes linear dispersion and the Gorbach-Flach (GF) lattice, which shares the same on-site potential but its dispersion is purely nonlinear. In both models under the implementation of long-range interactions (LRI) we find that single-site excitations lead to special low-dimensional solutions, which are well described by the undamped Duffing oscillator. For random initial conditions we observe that the maximal Lyapunov exponent λ scales as N −0.12 in the KG model and as N −0.27 in the GF with LRI, suggesting in that case an approach to integrable behavior towards the thermodynamic limit. Furthermore, under LRI, their non-Gaussian momentum distributions are distinctly different from those of the FPU model.