Da-Sheng Mou, Jia-Hao Zhang, Yun-Hao Jia, Chao-Qing Dai
{"title":"ii型狄拉克光子晶格中多极孤子的传播动力学及分数衍射效应对孤子的影响","authors":"Da-Sheng Mou, Jia-Hao Zhang, Yun-Hao Jia, Chao-Qing Dai","doi":"10.1016/j.chaos.2024.115895","DOIUrl":null,"url":null,"abstract":"<div><div>By changing the depth of the waveguide and adjusting the band structure to make the bandgap appear, the influence of the integer- and fractional-order diffractions on two-dimensional spatial localized modes in the II-type Dirac photonic lattices are investigated. Under the nonlinear action, the linear topological mode is transformed into a set of topological gap solitons, which form stable integer-order fundamental and dipole solions, and unstable quadrupole solion. Stable fractional-order fundamental and dipole solions and metastable quadrupole solion are obtained by decreasing the Lévy index, and the propagation dynamics of these solitons are discussed. By comparing the integer-order with the fractional-order solitons, it is proved that the propagation constant as well as the Lévy index play a crucial role in the stability of soliton. The findings enable insightful studies of highly localized gap modes in linear nonlocality (fractional) physical systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"191 ","pages":"Article 115895"},"PeriodicalIF":5.6000,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Propagation dynamics of multipole solitons and influence of fractional diffraction effect on solitons in II-type Dirac photonic lattices\",\"authors\":\"Da-Sheng Mou, Jia-Hao Zhang, Yun-Hao Jia, Chao-Qing Dai\",\"doi\":\"10.1016/j.chaos.2024.115895\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>By changing the depth of the waveguide and adjusting the band structure to make the bandgap appear, the influence of the integer- and fractional-order diffractions on two-dimensional spatial localized modes in the II-type Dirac photonic lattices are investigated. Under the nonlinear action, the linear topological mode is transformed into a set of topological gap solitons, which form stable integer-order fundamental and dipole solions, and unstable quadrupole solion. Stable fractional-order fundamental and dipole solions and metastable quadrupole solion are obtained by decreasing the Lévy index, and the propagation dynamics of these solitons are discussed. By comparing the integer-order with the fractional-order solitons, it is proved that the propagation constant as well as the Lévy index play a crucial role in the stability of soliton. The findings enable insightful studies of highly localized gap modes in linear nonlocality (fractional) physical systems.</div></div>\",\"PeriodicalId\":9764,\"journal\":{\"name\":\"Chaos Solitons & Fractals\",\"volume\":\"191 \",\"pages\":\"Article 115895\"},\"PeriodicalIF\":5.6000,\"publicationDate\":\"2025-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos Solitons & Fractals\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0960077924014474\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077924014474","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Propagation dynamics of multipole solitons and influence of fractional diffraction effect on solitons in II-type Dirac photonic lattices
By changing the depth of the waveguide and adjusting the band structure to make the bandgap appear, the influence of the integer- and fractional-order diffractions on two-dimensional spatial localized modes in the II-type Dirac photonic lattices are investigated. Under the nonlinear action, the linear topological mode is transformed into a set of topological gap solitons, which form stable integer-order fundamental and dipole solions, and unstable quadrupole solion. Stable fractional-order fundamental and dipole solions and metastable quadrupole solion are obtained by decreasing the Lévy index, and the propagation dynamics of these solitons are discussed. By comparing the integer-order with the fractional-order solitons, it is proved that the propagation constant as well as the Lévy index play a crucial role in the stability of soliton. The findings enable insightful studies of highly localized gap modes in linear nonlocality (fractional) physical systems.
期刊介绍:
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.