{"title":"Dynamics of the Energy Center of a Long-Wave Low-Amplitude Disturbance in an Anharmonic One-Dimensional Lattice","authors":"S. A. Shcherbinin","doi":"10.1134/S0025654424606001","DOIUrl":null,"url":null,"abstract":"<p>The dynamics of a disturbance with finite energy in an infinite monatomic nonlinear one-dimensional lattice are analyzed. Based on the energy dynamics approach proposed earlier, we focus on such disturbance spatial characteristic as the position of its energy center. Restricting our analysis to long-wave low-amplitude disturbances, we investigate the dynamics of the α-FPU chain using its continuous version described by the KdV equation. We establish a connection of the Lagrangian and the energy of the original chain with the two conserving quantities of the KdV equation. Using these two quantities and the known properties of the KdV equation, we propose a method for determining the velocity of the energy center of the disturbance at large times based on the initial conditions.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 5","pages":"3235 - 3243"},"PeriodicalIF":0.6000,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654424606001","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The dynamics of a disturbance with finite energy in an infinite monatomic nonlinear one-dimensional lattice are analyzed. Based on the energy dynamics approach proposed earlier, we focus on such disturbance spatial characteristic as the position of its energy center. Restricting our analysis to long-wave low-amplitude disturbances, we investigate the dynamics of the α-FPU chain using its continuous version described by the KdV equation. We establish a connection of the Lagrangian and the energy of the original chain with the two conserving quantities of the KdV equation. Using these two quantities and the known properties of the KdV equation, we propose a method for determining the velocity of the energy center of the disturbance at large times based on the initial conditions.
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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