An extension of the Wronskian technique for the multicomponent Wronskian solution to the vector nonlinear Schrödinger equation

Abstract

In this paper, the Wronskian technique is applied to the vector nonlinear Schrödinger equation with arbitrary m components, which arises from some applications in the multimode fibers, photorefractive materials, and Bose–Einstein condensates. Via the iterative algorithm based on the Darboux transformation, the (m+1)-component Wronskian solution is generated from the zero solution. The verification of the solution is finished by using the (m+1)-component Wronskian notation and new determinantal identities. With a set of N linearly independent solutions of the zero-potential Lax pair, the (m+1)-component Wronskian solution is found to be the representation of the bright N-soliton solution which contains (m+1)N parameters. For characterizing the asymptotic behavior of the generic bright N-soliton solution, an algebraic procedure is derived to obtain the explicit expressions of asymptotic solitons as t→∓∞.