{"title":"Optical soliton solutions and their nonlinear dynamics described by a novel time-varying spectral Hirota equation with variable coefficients","authors":"Xiuyan Wei, Shenwei Zong, Sheng Zhang","doi":"10.1007/s11082-024-07404-5","DOIUrl":null,"url":null,"abstract":"<p>The celebrated Hirota equation has important applications in nonlinear optics and quantum physics. This paper proposes a new type of time-varying spectral Hirota (tvsH) equation with variable coefficients and constructs its soliton solutions by extending the Riemann–Hilbert (RH) method. Specifically, Lax representation of the tvsH equation is first provided, which consists of time-varying spectral matrices, and the corresponding RH problem is further established by analyzing the Lax pair. Then, by combining inverse scattering and the spatiotemporal evolution of matrix vector solutions, an explicit expression for <i>n</i>-soliton solution of the tvsH equation is constructed in the absence of reflection potential. In addition, the collision soliton dynamics of the tvsH equation under isospectral and non-isospectral conditions are analyzed by modulating the time-varying coefficients. Most importantly, through the dynamic analysis of single and double solitons in the tvsH equation, we discover some new waveforms that have never been reported before, such as oscillating parabolic solitons and amplitude parabolic variation solitons. These waveforms may have significant theoretical and practical implications.</p>","PeriodicalId":720,"journal":{"name":"Optical and Quantum Electronics","volume":null,"pages":null},"PeriodicalIF":3.3000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optical and Quantum Electronics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s11082-024-07404-5","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
The celebrated Hirota equation has important applications in nonlinear optics and quantum physics. This paper proposes a new type of time-varying spectral Hirota (tvsH) equation with variable coefficients and constructs its soliton solutions by extending the Riemann–Hilbert (RH) method. Specifically, Lax representation of the tvsH equation is first provided, which consists of time-varying spectral matrices, and the corresponding RH problem is further established by analyzing the Lax pair. Then, by combining inverse scattering and the spatiotemporal evolution of matrix vector solutions, an explicit expression for n-soliton solution of the tvsH equation is constructed in the absence of reflection potential. In addition, the collision soliton dynamics of the tvsH equation under isospectral and non-isospectral conditions are analyzed by modulating the time-varying coefficients. Most importantly, through the dynamic analysis of single and double solitons in the tvsH equation, we discover some new waveforms that have never been reported before, such as oscillating parabolic solitons and amplitude parabolic variation solitons. These waveforms may have significant theoretical and practical implications.
期刊介绍:
Optical and Quantum Electronics provides an international forum for the publication of original research papers, tutorial reviews and letters in such fields as optical physics, optical engineering and optoelectronics. Special issues are published on topics of current interest.
Optical and Quantum Electronics is published monthly. It is concerned with the technology and physics of optical systems, components and devices, i.e., with topics such as: optical fibres; semiconductor lasers and LEDs; light detection and imaging devices; nanophotonics; photonic integration and optoelectronic integrated circuits; silicon photonics; displays; optical communications from devices to systems; materials for photonics (e.g. semiconductors, glasses, graphene); the physics and simulation of optical devices and systems; nanotechnologies in photonics (including engineered nano-structures such as photonic crystals, sub-wavelength photonic structures, metamaterials, and plasmonics); advanced quantum and optoelectronic applications (e.g. quantum computing, memory and communications, quantum sensing and quantum dots); photonic sensors and bio-sensors; Terahertz phenomena; non-linear optics and ultrafast phenomena; green photonics.