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

自然界中的过程，有时也包括社会中的过程，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相互关联。如果通过这些方程描述的过程是复杂的，那么通常会发生的是一种混乱的情况，并不断增加，就像某人的家没有得到清理。但在极少数情况下，复杂的微分方程描述的过程是自动保持秩序的，即结构不会溶解或消散。这些结构被称为孤子。例如，如果有人试图通过光纤电缆提交大量信息，并且不希望信息在途中混淆，那么所有这些都变得很重要。

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.