Generalized hydrodynamic limit for the box-ball system

[2003.06526] Generalized hydrodynamic limit for the box-ball system Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2003.06526 (math-ph) [Submitted on 14 Mar 2020 ( v1 ), last revised 14 May 2022 (this version, v2)] Title: Generalized hydrodynamic limit for the box-ball system Authors: David A. Croydon , Makiko Sasada View a PDF of the paper titled Generalized hydrodynamic limit for the box-ball system, by David A. Croydon and 1 other authors View PDF HTML (experimental) Abstract: We deduce a generalized hydrodynamic limit for the box-ball system, which explains how the densities of solitons of different sizes evolve asymptotically under Euler space-time scaling. To describe the limiting soliton flow, we introduce a continuous state-space analogue of the soliton decomposition of Ferrari, Nguyen, Rolla and Wang (cf. the original work of Takahashi and Satsuma), namely we relate the densities of solitons of given sizes in space to corresponding densities on a scale of 'effective distances', where the dynamics are linear. For smooth initial conditions, we further show that the resulting evolution of the soliton densities in space can alternatively be characterised by a partial differential equation, which naturally links the time-derivatives of the soliton densities and the 'effective speeds' of solitons locally. Subjects: Mathematical Physics (math-ph) ; Probability (math.PR) MSC classes: 37B15 (primary), 82C22, 82C23, 82C70 (secondary) Cite as: arXiv:2003.06526 [math-ph] (or arXiv:2003.06526v2 [math-ph] for this version) https://doi.org/10.48550/arXiv.2003.06526 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Commun. Math. Phys. 383, 427-463 (2021) Related DOI : https://doi.org/10.1007/s00220-020-03914-x Focus to learn more DOI(s) linking to related resources Submission history From: David Croydon [ view email ] [v1] Sat, 14 Mar 2020 01:07:59 UTC (43 KB) [v2] Sat, 14 May 2022 01:11:20 UTC (44 KB) Full-text links: Access Paper: View a PDF of the paper titled Generalized hydrodynamic limit for the box-ball system, by David A. Croydon and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2020-03 Change to browse by: math math.MP math.PR References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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