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

Zeng, Shijie; Liu, Yaqing

doi:10.1007/s11071-023-09156-5

Nonlinear Dyn

2023

DOI: 10.1007/s11071-023-09156-5

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

Shijie Zeng,

Yaqing Liu

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2024

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Cited by 2 publications

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Whitham modulation theory and Riemann problem for the Kundu–Eckhaus equation

Tan,

Zhang

2024

Physica D: Nonlinear Phenomena

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Whitham modulation theory and Riemann problem for the Kundu–Eckhaus equation

Tan,

Zhang

2024

Physica D: Nonlinear Phenomena

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Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation

Wu,

Tian

2024

Stud Appl Math

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In this work, we explore the Riemann problem of the Fokas–Lenells (FL) equation given initial data in the form of a step discontinuity by employing the Whitham modulation theory. The periodic wave solutions of the FL equation are characterized by elliptic functions along with the Whitham modulation equations. Moreover, we find that the signs for the velocities of the periodic wave solutions remain unchanged during propagation. Thus, when analyzing the propagation behavior of solutions, it is necessary to separately consider the clockwise (negative velocity) and counterclockwise (positive velocity) cases. In this regard, we present the classification of the solutions to the Riemann problem of the FL equation in both clockwise and counterclockwise cases for the first time.

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

Cited by 2 publications

References 42 publications

Whitham modulation theory and Riemann problem for the Kundu–Eckhaus equation

Whitham modulation theory and Riemann problem for the Kundu–Eckhaus equation

Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation

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