ncts

We analyze coherent structures in non-local dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto-Sivashinsky (KS) equation with an additional non-local term that contains stabilizing/destabilizing and dispersive parts. We show that sufficiently strong dispersion regularizes the chaotic dynamics of the KS equation and the solutions evolve into arrays of interacting pulses that can form bound states. We analyze the asymptotic characteristics of such pulses and show that their tails tend to zero algebraically but not exponentially as for the local gKS equation. We develop a weak-interaction theory and show that the standard first-neighbor approximation is not applicable anymore. It is then essential to take into account long-range interactions due to the algebraic decay of the tails of the pulses. We also develop numerical continuation techniques to explore bifurcation diagrams in systems possessing translational symmetry, including traveling waves and spatially time-periodic solutions. We find that each bound state bifurcates from the primary branch when continuing with respect to the domain size, and we then construct full bifurcation diagrams taking into account all the bound states.