J Cuevas, NI Karachalios and F Palmero (pdf copy 1MB)
We discuss the existence of breathers and of energy thresholds for their formation in DNLS lattices with linear and nonlinear impurities. In the case of linear impurities we present some new results concerning important differences between the attractive and repulsive impurity which is interplaying with a power nonlinearity. These differences concern the coexistence or the existence of staggered and unstaggered breather profile patterns. We also distinguish between the excitation threshold (the positive minimum of the power observed when the dimension of the lattice is greater or equal to some critical value) and explicit analytical lower bounds on the power (predicting the smallest value of the power a discrete breather one-parameter family), which are valid for any dimension. Extended numerical studies in one, two and three dimensional lattices justify that the theoretical bounds can be considered as existence thresholds for the frequency parametrized families. The discussion reviews and extends the issue of the excitation threshold in lattices with nonlinear impurities while the concept of the existence energy threshold (with respect to the kinetic energy) is also discussed for traveling pulses in FPU lattices.
Applicable Analysis 89(9): 1351-1385, September 2010. DOI: 10.1080/00036810903277135