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Conservation laws, soliton solutions and modulation instability for the coupled Gerdjikov–Ivanov equations

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Abstract

In this paper, we investigate the coupled Gerdjikov–Ivanov equations, which have the physical applications in nonlinear optics. The mass, energy and momentum conservation laws are obtained. Through the Hirota method, bright one- and two-soliton solutions are obtained. Interactions between two bright solitons are verified to be elastic through the asymptotic analysis. The oblique interactions and bound states of solitons are analyzed. The condition of modulation instability of the plane-wave solutions is given through the linear stability analysis.

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Acknowledgements

This work has been supported by the National Natural Science Foundations of China (Grant No. 11801597).

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Authors and Affiliations

  1. School of Science, Minzu University of China, Beijing, 100081, China

    Yu-Feng Wang

  2. School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, China

    Yi-Tong Pei

  3. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Bo-Ling Guo

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  1. Yu-Feng Wang
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  2. Yi-Tong Pei
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  3. Bo-Ling Guo
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Correspondence to Yi-Tong Pei.

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Wang, YF., Pei, YT. & Guo, BL. Conservation laws, soliton solutions and modulation instability for the coupled Gerdjikov–Ivanov equations. Z. Angew. Math. Phys. 74, 84 (2023). https://doi.org/10.1007/s00033-023-01981-3

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