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

自然界和社会中的过程有时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相互关联。如果要用这些方程描述的过程很复杂，那么通常会发生的是一种混乱的出现，并不断增加，就像有人的家经常没有打扫一样。但在极少数情况下，复杂的微分方程描述了自动维持秩序的过程，即结构不溶解或消散的过程。这些结构被称为孤子。所有这些都变得很重要，例如，如果一个人试图通过光纤电缆提交大量信息，并且不希望信息在传输过程中混淆。

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.