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

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Abstract

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 Schrödinger 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.

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Acknowledgements

This work has been supported by the BUPT Excellent Ph.D. Students Foundation under No. CX2021227, by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11805020, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Meng Wang & Bo Tian

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  1. Meng Wang
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Correspondence to Bo Tian.

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Wang, M., Tian, B. In an inhomogeneous multicomponent optical fiber: Lax pair, generalized Darboux transformation and vector breathers for a three-coupled variable-coefficient nonlinear Schrödinger system. Eur. Phys. J. Plus 136, 1002 (2021). https://doi.org/10.1140/epjp/s13360-021-01918-7

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