{"title":"非均匀非均质 PT 对称非线性介质中的色散管理和光学孤子工程","authors":"K. Manikandan , K. Sakkaravarthi , S. Sabari","doi":"10.1016/j.physd.2024.134388","DOIUrl":null,"url":null,"abstract":"<div><div>Studies on optical solitons in inhomogeneous media continue to attract immense interest. This work is devoted to exploring the evolution dynamics of solitons in inhomogeneous nonuniform optical media with parity-time reversal <span><math><mrow><mo>(</mo><mi>PT</mi><mo>)</mo></mrow></math></span>-symmetric rational potential and variable dispersion through explicit solutions. For this purpose, we consider a variable-coefficient nonlinear Schrödinger (vcNLS) equation containing <span><math><mi>PT</mi></math></span>-symmetric rational potential consisting of constant nonlinearity and longitudinally-varying dispersion and tapering effects. By implementing a similarity transformation, one of the efficient methods to analyze variable-coefficient (non-autonomous) nonlinear models, we construct explicit soliton (similariton) solutions and investigate deformations occurring in the characteristics of the optical solitons resulting from various dispersion modulations. Notably, we unravel the dynamical changes in the amplitude, width, shape, speed/velocity, and localization of solitons for periodic, localized well/barrier-type, and step-like dispersion modulations leading to periodic, localized, and single-step suppression or amplification, broadening and narrowing of width, and advancing or delaying the transitions during soliton propagation in inhomogeneous media. Besides, we execute a direct numerical experiment to validate the identified analytical findings. The observed results shall enhance the understanding of solitons in inhomogeneous <span><math><mi>PT</mi></math></span>-symmetric media. As future perspectives, the present analysis can be extended to study the deformation dynamics of several other nonlinear waves in inhomogeneous media and their experimental realizations in the context of optics and other fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134388"},"PeriodicalIF":2.7000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dispersion management and optical soliton engineering in nonuniform inhomogeneous PT-symmetric nonlinear media\",\"authors\":\"K. Manikandan , K. Sakkaravarthi , S. Sabari\",\"doi\":\"10.1016/j.physd.2024.134388\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Studies on optical solitons in inhomogeneous media continue to attract immense interest. This work is devoted to exploring the evolution dynamics of solitons in inhomogeneous nonuniform optical media with parity-time reversal <span><math><mrow><mo>(</mo><mi>PT</mi><mo>)</mo></mrow></math></span>-symmetric rational potential and variable dispersion through explicit solutions. For this purpose, we consider a variable-coefficient nonlinear Schrödinger (vcNLS) equation containing <span><math><mi>PT</mi></math></span>-symmetric rational potential consisting of constant nonlinearity and longitudinally-varying dispersion and tapering effects. By implementing a similarity transformation, one of the efficient methods to analyze variable-coefficient (non-autonomous) nonlinear models, we construct explicit soliton (similariton) solutions and investigate deformations occurring in the characteristics of the optical solitons resulting from various dispersion modulations. Notably, we unravel the dynamical changes in the amplitude, width, shape, speed/velocity, and localization of solitons for periodic, localized well/barrier-type, and step-like dispersion modulations leading to periodic, localized, and single-step suppression or amplification, broadening and narrowing of width, and advancing or delaying the transitions during soliton propagation in inhomogeneous media. Besides, we execute a direct numerical experiment to validate the identified analytical findings. The observed results shall enhance the understanding of solitons in inhomogeneous <span><math><mi>PT</mi></math></span>-symmetric media. As future perspectives, the present analysis can be extended to study the deformation dynamics of several other nonlinear waves in inhomogeneous media and their experimental realizations in the context of optics and other fields.</div></div>\",\"PeriodicalId\":20050,\"journal\":{\"name\":\"Physica D: Nonlinear Phenomena\",\"volume\":\"470 \",\"pages\":\"Article 134388\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica D: Nonlinear Phenomena\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167278924003385\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003385","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Dispersion management and optical soliton engineering in nonuniform inhomogeneous PT-symmetric nonlinear media
Studies on optical solitons in inhomogeneous media continue to attract immense interest. This work is devoted to exploring the evolution dynamics of solitons in inhomogeneous nonuniform optical media with parity-time reversal -symmetric rational potential and variable dispersion through explicit solutions. For this purpose, we consider a variable-coefficient nonlinear Schrödinger (vcNLS) equation containing -symmetric rational potential consisting of constant nonlinearity and longitudinally-varying dispersion and tapering effects. By implementing a similarity transformation, one of the efficient methods to analyze variable-coefficient (non-autonomous) nonlinear models, we construct explicit soliton (similariton) solutions and investigate deformations occurring in the characteristics of the optical solitons resulting from various dispersion modulations. Notably, we unravel the dynamical changes in the amplitude, width, shape, speed/velocity, and localization of solitons for periodic, localized well/barrier-type, and step-like dispersion modulations leading to periodic, localized, and single-step suppression or amplification, broadening and narrowing of width, and advancing or delaying the transitions during soliton propagation in inhomogeneous media. Besides, we execute a direct numerical experiment to validate the identified analytical findings. The observed results shall enhance the understanding of solitons in inhomogeneous -symmetric media. As future perspectives, the present analysis can be extended to study the deformation dynamics of several other nonlinear waves in inhomogeneous media and their experimental realizations in the context of optics and other fields.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.