离散与连续非线性耦合薛定谔系统的矢量畸形波解的构造及相互作用研究

项目名称： 离散与连续非线性耦合薛定谔系统的矢量畸形波解的构造及相互作用研究

项目编号： No.11201302

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 张海强

作者单位： 上海理工大学

项目金额： 22万元

中文摘要： 离散与连续非线性耦合薛定谔系统是海洋和非线性光学等工程技术和自然科学领域中具有广泛应用背景的可积非线性模型。作为一种特殊的非线性波- - 畸形波，由于它在非线性光学和海洋等领域拥有非常重要的实际应用价值，从而最近对畸形波的研究引起了极大关注。本项目首先解决如何构建离散与连续非线性耦合薛定谔系统的高阶矢量有理畸形波解的问题。其次，借助计算机符号计算，提出讨论该系统矢量畸形波解的数学结构以及畸形波之间相互作用的代数算法，从而可以弄清畸形波的基本特性和动力学机制。结合离散与连续非线性耦合薛定谔系统的物理应用背景，采用解析研究和数值计算分析相结合的方法来探索研究矢量畸形波在自然科学和工程技术中的应用。

中文关键词： 畸形波；达布变换；时空结构；动力学分析；

英文摘要： Discrete and continuous nonlinear coupled Schr?dinger systems are the integrable models and arise in many engineering settings and natural science including ocean and nonlinear optics. As one specific type of nonlinear waves, rogue waves have attracted considerable interest for their significant practical applicability in ocean and nonlinear optics fields. This research project firstly solves how to construct the solutions of high-order vector rational rogue wave in discrete and continuous nonlinear coupled Schr?dinger systems. Furthermore, via computerized symbolic computation, we will propose the algebra arithmetic about analyzing the mathematical structure of vector rogue wave solutions and discussing their interactions in discrete and continuous nonlinear coupled Schr?dinger systems. The basic properties and nonlinear dynamics of vector rogue waves can be analyzed based on the obtained rational solutions and algebra arithmetic. Considering the physical applied setting of disctete and continuous nonlinear coupled Schr?dinger systems, we will also explore and investigate the practical applications of vector rogue waves in natural science and engineering fields by combining the analytic study and numerical calculation methods.

英文关键词： rogue waves；Darboux transformation；temporal–spatial structures；dynamic analysis；