Vector multi-rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations in an alpha helical protein

In this paper, we investigate the vector multi-rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations, which describe the dynamics of an alpha helical protein with the nearest and next-nearest neighbor interactions and interspine coupling. Via the Darboux-dressing transformation, the vector multi-rogue-wave solutions are derived. Based on such solutions, we present the single vector rogue wave, vector rogue wave pair and triple vector rogue wave graphically. We show that a four-petaled rogue wave with two humps and two valleys appears in two components, while the other component has an eye-shaped rogue wave. Existing time of the rogue wave decreases with the strength of higher-order linear and nonlinear effects in the alpha helical protein. We also obtain the separated and interacting vector rogue wave pairs, as well as the triple vector rogue waves. Moreover, we verify the baseband modulation instability through the linear stability analysis.