关键词: three-coupled fourth-order nonlinear Schrödinger system, interactions of degenerate solitons, asymptotic analysis

Abstract: We investigate the alpha helical protein structure characterized by fourth-order interspine coupling, focusing on a three-coupled fourth-order nonlinear Schröinger 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 are retained upon the interactions. Elastic interactions between two degenerate solitons exhibiting four curve-type asymptotic solitons are depicted. When the lattice parameter $\beta$ changes, the velocities of the two degenerate solitons also 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 also presented. Interaction among two two-degenerate solitons with two spectral parameters is shown. The relative distance between two asymptotic solitons exhibits logarithmic growth with $|t|$, where $t$ represents the retarded time. Acceleration of soliton separation decays exponentially with relative distance, and eventually approaches zero. Phase shifts depend on $t$.

Key words: three-coupled fourth-order nonlinear Schrödinger system, interactions of degenerate solitons, asymptotic analysis