Semi-discrete DNA breather in Peyrard–Bishop–Dauxois model with fifth-order-approximation Morse potential

We discuss the existence of DNA breather in helicoidal Peyrard–Bishop–Dauxois model with fifth-order-approximation Morse potential based on semi-discrete approximation. This approximation handles the cases which are not admitted in the previous model with fourth-order-approximation Morse potential. It is found that the associated DNA breather is governed by Quintic Nonlinear Schrödinger equation with restricted parameter set. We give an example to explain its existence and dynamics, and confirm it by numerical integration of the discrete equation of motion with full Morse potential. Collision dynamics between the two contra-propagating Quintic DNA breathers is also discussed.