{"title":"On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range","authors":"Benjamin Ingimarson, Robert L. Pego","doi":"10.1137/23m1607209","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 808-830, June 2024. <br/> Abstract. We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces [math]. The inverse-cube case corresponds to Calogero–Moser systems which are well known to be completely integrable for any finite number of particles. The formal long-wave limit for unidirectional waves in these lattices is the Korteweg–de Vries equation if [math], but with [math] it is a nonlocal dispersive PDE that reduces to the Benjamin–Ono equation for [math]. For the infinite Calogero–Moser lattice, we find explicit formulas that describe solitary and periodic traveling waves.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1607209","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 808-830, June 2024. Abstract. We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces [math]. The inverse-cube case corresponds to Calogero–Moser systems which are well known to be completely integrable for any finite number of particles. The formal long-wave limit for unidirectional waves in these lattices is the Korteweg–de Vries equation if [math], but with [math] it is a nonlocal dispersive PDE that reduces to the Benjamin–Ono equation for [math]. For the infinite Calogero–Moser lattice, we find explicit formulas that describe solitary and periodic traveling waves.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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