权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Interaction of nonlinear waves

非线性波的相互作用

基本信息

批准号：
36465-2006
负责人：
Kovalyov, Mikhail
金额：
$ 0.73万
依托单位：
University of Alberta
依托单位国家：
加拿大
项目类别：
Discovery Grants Program - Individual
财政年份：
2008
资助国家：
加拿大
起止时间：
2008-01-01 至 2009-12-31
项目状态：
已结题

来源：
https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=390136
关键词：
Interaction nonlinear waves

项目摘要

The beauty of the rainbow is just a spectacular manifestation of the physical phenomenon of spectral decomposition, the phenomenon of the sunlight spliting up into simplest components or basic colors. A beam of light of sufficiently arbitrary origin may be decomposed into components and vice versa the components may be combined together to obtain any hue or color. Mathematically the combinations of basic colors are expressed by means of sums of functions describing basic colors with each function entering the sum with a certain coefficient. Phenomena that can be broken up into simple components and then reconstructed from these components in such a manner are called linear phenomena. In nature, however, not all phenomena are linear, most phenomena are actually nonlinear. So the question arises whether it is possible to break up functions describing nonlinear phenomena into simplest components and whether it is possible to combine the simple components to construct such functions. The mathematical description of this would be significantly more complicated than that of linear phenomena. In the proposal we consider the nonlinear phenomena described by what mathematicians call integrable systems. Such systems give rise to solitons. In the absence of solitons the functions describing them may be decomposed into nonlinear components analogous to basic colors of light. These components describing the simplest waves may be combined together to obtain functions describing a large variety of phenomena.

彩虹之美只是光谱分解这一物理现象的一种壮观的表现。光谱分解是指太阳光分解成最简单的成分或基本颜色的现象。一束光线的来源是任意的，它可以分解成各种成分，反之亦然，这些成分可以组合在一起，得到任何色调或颜色。在数学上，基本颜色的组合通过描述基本颜色的函数的和来表示，每个函数以一定的系数进入和。能被分解成简单成分，然后以这种方式从这些成分中重建的现象被称为线性现象。然而，在自然界中，并非所有的现象都是线性的，大多数现象实际上是非线性的。因此，问题就出现了：是否有可能把描述非线性现象的函数分解成最简单的分量，以及是否有可能把这些简单分量联合收割机组合起来构成这样的函数。这种现象的数学描述要比线性现象复杂得多。在这个提议中，我们考虑数学家称之为可积系统的非线性现象，这种系统会产生孤子。在没有孤立子的情况下，描述孤立子的函数可以分解成类似于光的基本颜色的非线性分量，这些描述最简单波的分量可以组合在一起，得到描述各种现象的函数。