Abstract
Under investigation in this paper is the variable coefficient three-coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of solitonic excitations along three-spine [Formula: see text]-helical protein with inhomogeneous effect. Via the Hirota method and symbolic computation, the exact two-bright-one-dark (TBD) and one-bright-two-dark (BTD) soliton solutions are constructed analytically. The propagation properties are discussed for TBD and BTD solitons when the variable coefficient is a hyperbolic secant function. Figures are plotted to reveal the following interactions of TBD and BTD two solitons: (1) Evolution without interactions of double-parabola-shaped solitons, of double-[Formula: see text]-shaped solitons and of parabola-[Formula: see text]-shaped solitons; (2) Evolution with periodic interaction of double-parabola-shaped solitons and of parabola-[Formula: see text]-shaped solitons; (3) Collision of double-[Formula: see text]-shaped solitons and of parabola-[Formula: see text]-shaped solitons.
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