Bright N-Soliton Solutions to the Vector Hirota Equation from Nonlinear Optics with Symbolic Computation

Under investigation in this paper is the vector Hirota (VH) equation which governs the simultaneous propagation of multiple interacting femtosecond pulses in a certain type of coupled optical waveguides. By the Nth iterated Darboux transformation starting from the zero potential, the VH equation is found to admit the bright N-soliton solutions in terms of the multi-component Wronskian. Asymptotic formulae of the bright N-soliton solutions are derived for any given set of spectral parameters, which allows us to directly analyze the collision dynamics of VH solitons. Via symbolic computation, some collision properties possessed by the two- and three-soliton solutions are revealed from four aspects: the asymptotic patterns of the colliding solitons, parametric conditions for the amplitude-preserving collisions, phase shifts induced by the vector-soliton collisions, and soliton state changes described by the generalized linear fractional transformations.