In an inhomogeneous multicomponent optical fiber: Lax pair, generalized Darboux transformation and vector breathers for a three-coupled variable-coefficient nonlinear Schrodinger system

Optical fibers are used in the optical sensors, optical imaging, ultrafast lasers and high-speed remote communications. In this paper, a three-coupled variable-coefficient nonlinear Schrodinger system, which models the attenuation or amplification of the picosecond pulses in an inhomogeneous multicomponent optical fiber with different polarizations or frequencies, is researched. In respect to the slowly varying envelopes of optical modes, we construct a Lax pair. Based on our Lax pair, we obtain the Nth-order generalized Darboux transformation, where N is a positive integer. We acquire the first- and second-order vector breather solutions according to the generalized Darboux transformation. We present the propagation of the first- and second-order vector breathers, as well as analyze the effects of the group velocity dispersion and nonlinearity coefficients on these vector breathers. Our results may provide some theoretical help for the future research on the adjustment of the vector breathers in an inhomogeneous multicomponent optical fiber.