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

Yuping Sun, Yushu Zeng and Shihui Zhu

Chaos, Solitons & Fractals, 2025, vol. 199, issue P1

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.

Keywords: Third-order Kaup–Newell equation; Whitham modulation theory; Finite-gap integration method; Riemann problem; Dispersive shock wave (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006484

DOI: 10.1016/j.chaos.2025.116635

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