LAUSR

In the present paper, we study the fundamental mechanism of unidirectional energy transport in the symmetric, weakly dissipative system of two coupled nonlinear oscillators and weakly coupled oscillatory chains. We demonstrate that under particular choice of system parameters the model under consideration allows the irreversible transfer of energy from the initially excited oscillator to the initially resting one. In the second part of the paper, we implement the mechanism for control of spatially localized nonlinear waves (discrete breathers) in weakly dissipative, coupled oscillatory chains. This mechanism is implemented on the symmetric system of two weakly dissipative, non-linearly coupled oscillatory chains. Using the regular multi-scale asymptotic analysis, we derive the slow flow system. Further applying the method of collective coordinates on the slow flow system, we were able to describe analytically the mechanism of unidirectional inter-chain transport of static breathers. In general, the analytical method developed in the paper allows one to predict the special regions in the parametric space corresponding to the formation of the aforementioned regimes of irreversible energy transfer in the system of non-linearly coupled oscillators and oscillatory chains.