Abstract
Abstract In this article, we investigate a fourth-order nonlinear Schrödinger equation, which governs the Davydov solitons in the alpha helical protein with higher-order effects. By virtue of the generalised Darboux transformation, higher-order rogue-wave solutions are derived. Propagation and interaction of the rogue waves are analysed: (i) Coefficients affect the existence time of the first-order rogue waves; (ii) coefficients affect the interaction time of the second- and third-order rogue waves; (iii) direction of the rogue-wave propagation remain unchanged after interaction.
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