参数驱动非线性薛定谔方程的直接散射研究
The direct scattering study of the parametrically driven nonlinear Schrödinger equation
摘要：
术语“直接散射研究”是指计算和分析相关的Zakharov-Shabat（ZS）本征值问题的离散本征值。直接散射研究应用于参数驱动的非线性薛定谔方程中作为吸引子产生的含时振荡孤子。四种不同类型的参数空间内的吸引子被确定，每一个具有独特的孤子内容结构。这些结构包括辐射诱导的非线性模和孤子复合结构。利用不同类型的吸引子来研究吸引子对阻尼和驱动参数的依赖性。倍周期分岔被证明是影响振荡孤子的辐射发射。孤子复杂的结构和辐射的时空混沌的形成中的作用也被确定。
英文摘要：
The term "direct scattering study" refers to the calculation and analysis of the discrete eigenvalues of the associated Zakharov-Shabat (ZS) eigenvalue problem. The direct scattering study was applied to time-dependent oscillating solitons that arise as attractors in the parametrically driven nonlinear Schrödinger equation. Four different types of attractors within the parameter space are identified, each with a unique soliton content structure. These structures include radiation-induced nonlinear modes and soliton complex structures. The different types of attractors are used to characterise the dependence of the attractors on damping and driving parameters. Period-doubling bifurcations are shown to affect the radiation emissions of oscillating solitons. The role of soliton complex structures and radiation in the formation of spatio-temporal chaos is also identified.
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