Gap solitons in gapless coupled chains

We consider a system consisting of two coupled atomic chains in a substrate potential; it is assumed that the atoms do not interact along one of the chains. We demonstrate that intersection of the dispersion curves of the two uncoupled subsystems is a general mechanism producing gap envelope solitons in the presence of a weak coupling and weak nonlinearity. Moreover, considering the model in which one subsystem is degenerate (due to the absence of the interaction inside the corresponding chain, its dispersion curve is a straight horizontal line), we find a new effect: while the width of the gap in the linearized system is equal to zero (or is very small), the nonlinearity produces an effective gap in which the solitons exist. The corresponding soliton solutions are found in an exact analytical form.