{"title":"The <i>κ</i>-Deformed Calogero-Leyvraz Lagrangians and Applications to Integrable Dynamical Systems.","authors":"Partha Guha","doi":"10.3390/e24111673","DOIUrl":null,"url":null,"abstract":"<p><p>The Calogero-Leyvraz Lagrangian framework, associated with the dynamics of a charged particle moving in a plane under the combined influence of a magnetic field as well as a frictional force, proposed by Calogero and Leyvraz, has some special features. It is endowed with a Shannon \"entropic\" type kinetic energy term. In this paper, we carry out the constructions of the 2D Lotka-Volterra replicator equations and the N=2 Relativistic Toda lattice systems using this class of Lagrangians. We take advantage of the special structure of the kinetic term and deform the kinetic energy term of the Calogero-Leyvraz Lagrangians using the κ-deformed logarithm as proposed by Kaniadakis and Tsallis. This method yields the new construction of the κ-deformed Lotka-Volterra replicator and relativistic Toda lattice equations.</p>","PeriodicalId":520609,"journal":{"name":"Entropy (Basel, Switzerland)","volume":" ","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9689000/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entropy (Basel, Switzerland)","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3390/e24111673","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The Calogero-Leyvraz Lagrangian framework, associated with the dynamics of a charged particle moving in a plane under the combined influence of a magnetic field as well as a frictional force, proposed by Calogero and Leyvraz, has some special features. It is endowed with a Shannon "entropic" type kinetic energy term. In this paper, we carry out the constructions of the 2D Lotka-Volterra replicator equations and the N=2 Relativistic Toda lattice systems using this class of Lagrangians. We take advantage of the special structure of the kinetic term and deform the kinetic energy term of the Calogero-Leyvraz Lagrangians using the κ-deformed logarithm as proposed by Kaniadakis and Tsallis. This method yields the new construction of the κ-deformed Lotka-Volterra replicator and relativistic Toda lattice equations.
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