Bright N-soliton solutions in terms of the triple Wronskian for the coupled nonlinear Schrödinger equations in optical fibers

The coupled nonlinear Schrödinger (NLS) equations are usually used to describe the dynamics of two-component solitons in optical fibers. Via the Darboux transformation, the coupled NLS equations of the Manakov type are found to have triple Wronskian solutions. Proof is finished by virtue of some new triple Wronskian identities. By solving the zero-potential Lax pair, the triple Wronskian solutions give the bright N-soliton solutions which are characterized by 3N complex parameters. To obtain an understanding of the asymptotic behavior of the bright N-soliton solutions with arbitrary N, some algebraic properties of the triple Wronskian are analyzed and an algebraic procedure is presented to derive the explicit expressions of the asymptotic solitons as t → ∞.