论具有无限范围力的粒子晶格中的长波和孤子

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-05-03 DOI:10.1137/23m1607209

Benjamin Ingimarson, Robert L. Pego

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引用次数: 0

摘要

SIAM 应用数学杂志》第 84 卷第 3 期第 808-830 页，2024 年 6 月。摘要。我们研究由粒子组成的无限一维晶格上的波，每个粒子都通过幂律力与其他粒子相互作用[数学]。反立方情况对应于 Calogero-Moser 系统，众所周知，该系统对于任何有限数量的粒子都是完全可积分的。这些晶格中单向波的形式长波极限是[math]的 Korteweg-de Vries 方程，但在[math]的情况下，它是一个非局部色散 PDE，可以简化为[math]的 Benjamin-Ono 方程。对于无限卡洛吉罗-莫泽晶格，我们找到了描述孤行波和周期行波的明确公式。

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On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range

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.

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

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.