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Step-like initial value and Whitham modulation theory of the Fokas–Lenells equation

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Abstract

The step-like initial value problem of the Fokas–Lenells equation is discussed based on Whitham modulation theory. Via the finite-gap integration method, the zero-phase, one-phase, N-phase solutions, and corresponding Whitham equation are obtained. Analytical and graphical methods are used to provide elementary wave structures of rarefaction waves and dispersive shock waves, which allows the classification of all wave structures that evolve from initial discontinuities. Finally, two typical Riemann problems are solved and represented graphically.

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Acknowledgements

This work is supported by the Beijing Natural Science Foundation (No. 1222005), Qin Xin Talents Cultivation Program of Beijing Information Science and Technology University (QXTCP C202118).

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  1. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, China

    Shijie Zeng & Yaqing Liu

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  1. Shijie Zeng
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SZ: Writing-original daft, Software. YL: Supervision, Investigation.

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Correspondence to Yaqing Liu.

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Zeng, S., Liu, Y. Step-like initial value and Whitham modulation theory of the Fokas–Lenells equation. Nonlinear Dyn 112, 1365–1376 (2024). https://doi.org/10.1007/s11071-023-09156-5

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