Biological multi-rogue waves in discrete nonlinear Schrödinger equation with saturable nonlinearities

•Discrete Multi-Rogue Waves (DMRW), representing the localization of vibrational energy in protein chain, are found numerically.•The higher order saturable nonlinearity of DNLS promotes the increase in the short-living RW.•The higher order saturable nonlinearity of DNLS promotes the decrease in amplitude of the long-living RW.

The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.