Wave turbulence and collective behavior models for wave equations with\n short- and long-range interactions

2021/10/14 by Alejandro B. Aceves, Ricardo Alonso, Aceves, Alejandro +4
Computer Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Opinion Dynamics and Social Influence

paper · pdf · doi:10.48550/arxiv.2110.07830

openalex publication_date 2021/10/14 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this work, we discuss a situation which could lead to both wave turbulence\nand collective behavior kinetic equations. The wave turbulence kinetic models\nappear in the kinetic limit when the wave equations have local differential\noperators. Viewing wave equations on the lattice as chains of anharmonic\noscillators and replacing the local differential operators (short-range\ninteractions) by non-local ones (long-range interactions), we arrive at a new\nVlasov-type kinetic model in the mean field limit under the molecular chaos\nassumption reminiscent of models for collective behavior in which anharmonic\noscillators replace individual particles.\n

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