波群演化与相互作用
Wave group evolution and interaction
摘要：
本论文主要研究在水动力实验室中，确定性畸形波产生的数学与物理问题。采用非线性薛定谔方程作为地面重力波包包络演化的数学模型。正如Benjamin和Feir（1967）在理论上预测和实验上观察到的那样，深水中的斯托克斯波在边带调制下是不稳定的。NLS方程的平面波解代表Stokes波的基本分量，在线性微扰理论下经历类似的调制不稳定性。这种扰动波的非线性扩展由有限背景上的孤子族（SFB）给出，其中精确的表达式是可用的，并且可以通过几种技术解析地导出。我们讨论的特点的SFB家庭作为一个主要的候选人畸形波事件。相应的物理波场表现出有趣的现象波前错位和相位奇异性。
英文摘要：
This thesis deals with mathematical and physical aspects of deterministic freak wave generation in a hydrodynamic laboratory. We adopt the nonlinear Schrödinger (NLS) equation as a mathematical model for the evolution of the surface gravity wave packet envelopes. As predicted theoretically and observed experimentally by Benjamin and Feir (1967), Stokes waves on deep water are unstable under a sideband modulation. The plane-wave solution of the NLS equation, which represents the fundamental component of the Stokes wave, experiences a similar modulational instability under the linear perturbation theory. A nonlinear extension for this perturbed wave is given by the family of Soliton on Finite Background (SFB), where an exact expression is available and can be derived analytically by several techniques. We discuss the characteristics of the SFB family as a prime candidate for freak wave events. The corresponding physical wave field exhibits intriguing phenomena of wavefront dislocation and phase singularity.
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