Soliton excitations in a three-spine alpha-helical protein chain with quintic non-linearity

We study the dynamics of a three-spine alpha-helical protein chain with quintic non-linearity. The dynamics is found to be governed by a perturbed three-coupled non-linear Schrödinger (NLS) equation. To investigate the solitonic aspects, we identify a completely integrable three-coupled cubic–quintic NLS equation by deriving the Lax pair of operators associated with it. In addition, we study the modulation instability aspects and obtain the conditions for soliton formation.