Lax connection and conserved quantities of quadratic mean field games

Thibault Bonnemain*, Thierry Gobron, Denis Ullmo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 Schrödinger 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.
Original languageEnglish
Article number083302
Number of pages14
JournalJournal of Mathematical Physics
Volume62
Issue number8
DOIs
Publication statusPublished - 1 Aug 2021

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