Gauge-invariant coherent structures and modulational instability in a stochastic Yajima–Oikawa system

Ahmed H. Arnous, Kamyar Hosseini, Muhammad Amin S. Murad, Yakup Yildirim and Nehad Ali Shah

Chaos, Solitons & Fractals, 2026, vol. 210, issue P1

Abstract: This paper investigates a stochastic Yajima–Oikawa long-wave–short-wave resonance system with multiplicative Stratonovich phase noise acting on the short-wave component. By embedding the Brownian motion into the carrier phase, we show that the stochastic perturbation is gauge-removable from the amplitude dynamics. Consequently, the traveling-wave reduction leads to a deterministic Duffing-type profile equation while the long-wave component is slaved to the short-wave intensity through an explicit algebraic relation. Using the associated Hamiltonian structure, we classify the admissible dynamical regimes and derive explicit solitary-wave solutions, kink-type amplitude waves with dark-notch intensity profiles on a nonzero background, and Jacobi elliptic periodic waves. The homoclinic, heteroclinic, and closed periodic trajectories of the reduced phase plane are directly connected with these wave families. We also perform a modulational-instability analysis of the continuous-wave background and prove that, for the present pure Stratonovich phase-noise model, the instability threshold and growth law coincide with those of the gauge-equivalent deterministic system. Finally, we derive phase-sensitive stochastic observables showing that Brownian phase noise produces exponential attenuation of the ensemble mean field and temporal correlation decay, whereas the short-wave intensity and the induced long-wave response remain deterministic. The results clarify how random carrier-phase fluctuations influence observable phase coherence without changing the leading-order coherent envelope mechanism.

Keywords: Stochastic Yajima–Oikawa system; Stratonovich phase noise; Coherent structures; Phase-plane analysis; Modulational instability (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p1:s096007792600768x

DOI: 10.1016/j.chaos.2026.118627

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