Several new analytical solutions for Davydov solitons in α-helix proteins

Abstract

Various forms of rational solitons, breathers, rogue wave, periodic wave and multiwave for Davydov solitons in [Formula: see text]-helix proteins are described in this paper. We will figure out periodic wave, rogue wave, multiwave, [Formula: see text]-shaped solutions, homoclinic breathers, kink cross rational solutions, periodic cross kink, periodic cross rational solitons, generalized breather, Akhmediev breather and Kuznetsov–Ma breather. We will also discuss some interactions between them. At the end, we will provide the graphical representation of our newly discovered solutions.