论文标题
松弛的连接和保守数量的二次平均野战游戏
Lax Connection and Conserved Quantities of Quadratic Mean Field Games
论文作者
论文摘要
平均现场游戏是最初在应用数学和工程中开发的一个相当新的字段，以便处理互动中大量受控代理或对象的动态。对于这些模型的大量模型，相关的方程系统与非线性schrödinger方程之间存在着深厚的关系，该方程允许对其解决方案的结构获得新的见解。在这项工作中，我们处理了此类系统的集成性的相关方面，在某些情况下展示了全部保守数量的层次结构，并带来了在这种特定情况下出现的一些新问题。
Mean Field Game is a rather new field initially developed in applied mathematics and engineering in order to deal with the dynamics of a large number of controlled agents or objects in interaction. For a large class of these models, there exists a deep relationship between the associated system of equations and the non linear Schrödinger equation, which allows to get new insights on the structure of their solutions. In this work, we deal with related aspects of integrability for such systems, exhibiting in some cases a full hierarchy of conserved quantities, and bringing some new questions which arise in this specific context.
