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Step-type initial value problem for the third-order Kaup–Newell equation

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  • Sun, Yuping
  • Zeng, Yushu
  • Zhu, Shihui

Abstract

In this paper, we utilize the Whitham theory and the finite-gap method to study the third-order Kaup–Newell (TOFKN) equation with step-like initial data. By analyzing the corresponding modulation equation, we obtain the 0-genus solution, 1-genus solutions, and wave’s structures of dispersive shock waves and rarefaction waves. Moreover, we investigate the wave structures and classifications of solutions of the TOFKN with discontinuous initial data in terms of the corresponding Riemann invariants and Riemann problem. These results can shed light on the nonlinear spatial beam propagation phenomenon in optics and may provide guidance for physical experiments to observe some new phenomenon.

Suggested Citation

  • Sun, Yuping & Zeng, Yushu & Zhu, Shihui, 2025. "Step-type initial value problem for the third-order Kaup–Newell equation," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006484
    DOI: 10.1016/j.chaos.2025.116635
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    References listed on IDEAS

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    1. Nikolay A. Kudryashov & Sofia F. Lavrova, 2024. "Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 12(11), pages 1-13, May.
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    Cited by:

    1. Xu, Shuwei & He, Jingsong, 2025. "Various rational solutions generated from the higher order Kaup–Newell type equation," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).

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