Lax connection and conserved quantities of quadratic mean field games

Mean field games is a new field developed simultaneously 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 Schrodinger equation, which allows us to get new insights into the structure of their solutions. In this work, we deal with the related aspects of integrability for such systems, exhibiting in some cases a full hierarchy of conserved quantities and bringing some new questions that arise in this specific context.

Automated summary

Mean field games is a newly developed field aiming to deal with the dynamics of a large number of controlled agents, showing deep relationship with the nonlinear Schrodinger equation in many cases and bringing new questions related to integrability in this specific context.