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Generalized coupled Fokas–Lenells equation: modulation instability, conservation laws, and interaction solutions

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Abstract

This paper focuses on the modulation instability, conservation laws, and interaction solutions of the generalized coupled Fokas–Lenells equation. Based on the theory of linear stability analysis, distribution pattern of modulation instability gain G in the (K, k) frequency plane is depicted, and the constraints for the existence of rogue waves are derived. Subsequently, we construct the infinitely many conservation laws for the generalized coupled Fokas–Lenells equation from the Riccati-type formulas of the Lax pair. In addition, the compact determinant expressions of the N-order localized wave solutions are given via generalized Darboux transformation, including higher-order rogue waves and interaction solutions among rogue waves with bright-dark solitons or breathers. These solutions are parameter controllable: \((m_i,n_i)\) and \((\alpha ,\beta )\) control the structure and ridge deflection of solution, respectively, while the value of |d| controls the strength of interaction to realize energy exchange. Especially, when \(d=0\), the interaction solutions degenerate into the corresponding order of rogue waves.

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Acknowledgements

We would like to express our sincere thanks to Professor Yong Chen for his valuable comments. The project is supported by the National Natural Science Foundation of China (No. 12005027), Postdoctoral Research Foundation of China (No. 2020M673116), and Natural Science Foundation of Chongqing (No. cstc2020jcyj-bshX0018).

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  1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Yunfei Yue

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Lili Huang

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Yue, Y., Huang, L. Generalized coupled Fokas–Lenells equation: modulation instability, conservation laws, and interaction solutions. Nonlinear Dyn 107, 2753–2771 (2022). https://doi.org/10.1007/s11071-021-07123-6

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