Dynamical analysis, and the effect of fractional parameters on optical soliton solution for Yajima–Oikawa model in short-wave and long-wave

Mohamed Abdalla, Md. Mamunur Roshid, Mohammad Safi Ullah and Ismail Hossain

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

Abstract: This manuscript provides a comprehensive study of the recently introduced Yajima–Oikawa model to describe the characteristics of the nonlinear resonant interaction between short-wave and long-wave. In this work, we focus on the bifurcation analysis, the chaotic nature with different chaos-detecting tools, and the impact of the fractional parameter on optical soliton solutions of the Yajima–Oikawa model. At first, we implement a transformation variable to adapt the YO model into ordinary differential equation form. To bifurcation analysis, the attained from converted into dynamical systems by using a Galilean transformation that uncovered essential equilibrium states and associated transitions. Secondly, we investigate the recurrence plots, power spectrum, bifurcation plot, return map, Lyapunov exponent, fractal dimension tool, strange attractor, and basin of attraction for the proposed model. Additionally, to obtain an exact soliton solution for the Yajima–Oikawa model, the modified F-expansion method also applies to a dependable treatment. Trigonometric, rational, and hyperbolic, rational functions are used to express the solutions. We discovered a range of new optical soliton solutions, each of which is highlighted by graphical simulations that highlight its unique properties and requirements for existence. Finally, we also check the numerical stability of the obtained solutions. Moreover, this paper offers novel insights on solitons in fields such as applied mathematics, fluid dynamics, and nonlinear wave theory, where these mathematical formulas are crucial for elucidating complex phenomena.

Keywords: Bifurcation analysis; Lyapunov exponent; Strange attractor; Basin of attraction; Yajima–Oikawa model; Short-wave and long-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:s0960077925007106

DOI: 10.1016/j.chaos.2025.116697

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