非线性海洋内波动力学特征的理论分析

The study on the formation, development and evolution of internal waves is important and hot topics in oceanology. Therefore from dynamics, study on phenomena of internal waves not only enrich and deepen the theory of internal waves, but also possesses value of practical applications. In this project, based on theories of soliton, stability, qualitative and waves, we theoretically analyze internal waves in the ocean, we hope make our characteristic and breakthrough work in the following four aspects: (1) Based on the soliton theory，we develop analytical methods to solve governing equations of internal waves, such that we construct internal solitary waves, quasi-periodic waves, rogue waves etc. (2) Based on the governing equations and analytical solutions of internal waves, we analyze generation mechanism and sources of internal waves. (3) Based on the analytical solutions obtained above, we analyze structures of internal waves and characteristic parameters. (4) Based on the governing equations and by using Lyapunov and qualitative theories, we theoretically analyze stability, asymptotic stability, global stability, Structural stability and breaking of internal waves. The results of this project will promote intersect of different subjects and provide new theory and methods for sea and oceanographic engineering

海洋内波的生成、发展和演变一直是物理海洋学研究的重点和热点。从动力学角度分析海洋内波各类现象不仅可以丰富和深化内波理论，而且具有实际的应用价值。本项目基于孤立子理论、稳定性理论、动力系统和波浪理论，解析分析海洋內波的动力学特征，在以下四个方面形成突破，做出有特色的高水平工作：（1）基于孤立子理论，发展求解內波控制模型的解析方法，由此构造內波控制模型的孤波解、拟周期波解、畸形波解等。（2）从內波控制模型和解析解出发，研究內波的生成机理和发源地。（3）从解析解出发，计算内波传播的振幅、波长、波速等特征参数。（4）直接从內波控制模型出发，利用李雅普诺夫理论和微分方程定性理论，分析内波的稳定、渐近稳定、大范围稳定，结构稳定和破碎现象。本项目通过将数学工具引入海洋内波研究，形成具有创新性的理论成果和方法，为海洋工程研究和结构设计提供必要的理论依据与分析方法。

非线性波的研究在海洋工程、物理学、流体力学、应用数学等诸多领域有重要应用。本项目基于孤立波理论、稳定性理论、动力系统和波浪理论，发展了求解水波控制模型的解析方法、从定性和定量角度研究了非线性波的动力学特征、轨道稳定、渐近稳定、长时间渐近性和破碎现象。通过本课题的实施，我们在国内外重要学术刊物发表SCI论文42篇，在科学出版社出版专著2部；培养博士后4名，博士研究生19名，研究成果达到了国际先进水平。在本研究课题的实施过程，充分发挥了课题组成员在数学方面的优势，将一些有效的数学方法引入了水波模型的研究，为解决有关非线性波和海洋工程领域的困难问题的解决提供了提供必要的理论依据与分析方法。