Applications of advances in computer algebra to studying classical integrable systems and various algebraic structures

自然界中的过程，有时是社会中的过程，都是通过变量来描述的，比如‘温度’、‘电场’或‘人口密度’。这些变量通过所谓的微分方程式相互联系。如果通过这些方程描述的过程是复杂的，那么通常发生的是一种无序开始并不断增加，就像一些人的家不经常得到清理一样。但在极少数情况下，复杂的微分方程式描述了自动维持秩序的过程，即结构不会溶解或消散。这些结构被称为孤子。例如，如果一个人试图通过光纤电缆提交大量信息，而不想让信息在传输过程中被混淆，那么所有这些都变得重要起来。

Processes in nature and sometimes in society are described through variables, like 'temperature', 'electric field' or 'population density'. These variables are related to each other through so-called differential equations. If the process to be described through these equations is complicated then what typically happens is that a kind of disorder sets in and increases constantly, like someones home that does not get cleaned up from time to time. But in rare cases complicated differential equations describe processes where order is maintained automatically, i.e. where structures do not dissolve or dissipate. These structures are called solitons. All this becomes important, for example, if one tries to submit gigantic amounts of information through a fibre optics cable and does not want the information to get mixed up on its way.