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Modulational instability and homoclinic orbit solutions in vector nonlinear Schr?dinger equation
摘要： Modulational instability has been used to explain the formation of breathers and rogue waves qualitatively. In this paper, we show modulational instability can be used to explain the structure of them in a quantitative way. In the first place, we develop a method to derive general forms for Akhmediev breathers, rogue waves and their multiple or high order ones in a N-component nonlinear Schr?dinger equations. The existence condition for each pattern is clarified clearly with a compact algebraic equation. Moreover, we show that the existence condition of ABs and RWs is consistent with the dispersion relation of the linear stability analysis on the background solution. The results further deepen our understanding on the quantitative relations between modulational instability and homoclinic orbits solutions.
关键词： general multi-high-order rogue wave,vector nonlinear Schr?dinger equation,modulational instability analysis,Akhmediev breathers
更新于2025-09-23 15:22:29
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Fermi-Pasta-Ulam-Tsingou Recurrence in Spatial Optical Dynamics
摘要： Celebrated as the Fermi-Pasta-Ulam-Tsingou (FPUT) problem, the reappearance of initial conditions in unstable and chaotic systems is one of the most controversial phenomena in nonlinear dynamics. Integrable models predict recurrence as exact solutions [1], but the difficulties involved in upholding integrability for a long dynamics has not allowed a quantitative experimental validation. Evidences of the recurrence of states have been reported from deep water waves [2] to optical fibers [3]. However, the observation of the FPUT dynamics as predicted by exact solutions of an underlying integrable model remains an open challenge. Here, we report the observation of the FPUT recurrence in spatial nonlinear optics and provide evidence that the recurrent behavior is ruled by the exact solution of the Nonlinear Schrodinger Equation [4]. We exploit a three-waves interferometric setup [Fig. 1(a)] to finely tune amplitude and phase of the single-mode input perturbation propagating in a pumped photorefractive medium [5]. We reveal how the unstable mode manifests the Akhmediev breathers (AB) profile [Fig.1(c)] and undergoes several growth and decay cycles [Fig. 1(b)] whose partial-period and phase-shift are determined by the initial excitation in remarkable agreement with the analytic NLSE theory [Fig.1(d-e)]. The deterministic properties of the return cycle allows us to achieve one of the basic aspirations of nonlinear dynamics: the reconstruction, after several return cycles, of the exact initial condition of the system [Fig. 1(f)], ultimately proving that the complex evolution can be accurately predicted in experimental conditions. This results extends predictive approaches to unstable wave regimes and maps a strategy to achieve the control of rogue waves [6] in environmental conditions. In general, our findings shed light on the foundations of the FPUT problem and represent a unique test for nonlinear wave theory, with broad implications in nonlinear optics, hydrodynamics and beyond.
关键词： Nonlinear Schrodinger Equation,spatial optical dynamics,Akhmediev breathers,Fermi-Pasta-Ulam-Tsingou recurrence,nonlinear dynamics
更新于2025-09-11 14:15:04