Degenerate solitons and asymptotic analysis for a three-coupled fourth-order nonlinear Schrödingier system in an alpha helical protein

Abstract Investigating the alpha helical protein structure characterized by the fourth-order interspine coupling, we focus on a three-coupled fourth-order nonlinear Schrödinger system. We introduce a generalized Darboux transformation, departing from the classical Darboux transformation. Based on this, we construct the two- and three-degenerate soliton solutions, and four-degenerate asymptotic soliton solutions. Based on the asymptotic analysis, we find that the amplitudes of interacting solitons have retained upon the interactions. Elastic interactions between two degenerate solitons exhibiting four curve-type asymptotic solitons are depicted. When lattice parameter β changes, the velocities of the two degenerate solitons change. Elastic interaction among three degenerate solitons comprising four curve-type asymptotic solitons and two line-type solitons is presented. Interaction among one soliton and two degenerate solitons with different velocities is shown. Elastic interaction among four degenerate solitons comprising eight curve-type asymptotic solitons is presented. Interaction among two two-degenerate solitons with two spectral parameters is presented. Relative distance between two asymptotic solitons exhibits logarithmic growth with | t |, where t represents the retarded time. Soliton separation acceleration decays exponentially with relative distance, eventually approachs zero. Phase shifts depend on t .