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Transformed nonlinear waves, state transitions and modulation instability in a three-component AB model for the geophysical flows

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Abstract

In this paper, we investigate a three-component AB model, which characterizes the baroclinic instability processes in the geophysical flows. Via the Darboux transformation, the breather solutions are derived. Then, we study the state transition and find that the breather solutions can be transformed into different kinds of stationary nonlinear waves, including the anti-dark soliton, multi-peak soliton, M-shaped soliton, W-shaped solitons and periodic waves. Moreover, by virtue of the second-order transformed solution, various nonlinear wave complexes are presented. Finally, we unveil the relationship between the modulation instability and state transition and show the existence regions for the transformed waves.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11875126, 11905061 and 11705290), Key scientific and technological projects in Henan Province (202102210363), Young Scholar Foundation of Zhongyuan University of Technology (2018XQG16). Lei Wang came up with the idea of this paper. Lei Wang was responsible for all physical analysis. Lei Wang and Han-Song Zhang wrote this paper. Han-Song Zhang was responsible for all simulations and calculations. Xin Wang and Xi-Yang Xie polished the language.

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  1. H. Zhang, L. Wang: These authors are co-first authors.

Authors and Affiliations

  1. School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

    Han-Song Zhang & Lei Wang

  2. College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, China

    Xin Wang

  3. Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China

    Xi-Yang Xie

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  1. Han-Song Zhang
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Zhang, HS., Wang, L., Wang, X. et al. Transformed nonlinear waves, state transitions and modulation instability in a three-component AB model for the geophysical flows. Nonlinear Dyn 102, 349–362 (2020). https://doi.org/10.1007/s11071-020-05964-1

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