Lax connection and conserved quantities of quadratic mean field games

Bonnemain, Thibault, Gobron, Thierry and Ullmo, Denis (2021) Lax connection and conserved quantities of quadratic mean field games. Journal of Mathematical Physics, 62 (8). 083302. ISSN 0022-2488

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Official URL: https://doi.org/10.1063/5.0039742

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.

Item Type: Article
Uncontrolled Keywords: Mathematical Physics, Statistical and Nonlinear Physics
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Rachel Branson
Date Deposited: 09 Aug 2021 10:53
Last Modified: 11 Aug 2021 09:01
URI: http://nrl.northumbria.ac.uk/id/eprint/46879

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