Dissipative Soliton Resonance: Adiabatic Theory and Thermodynamics

IF 1.4 4区 物理与天体物理 Q2 MATHEMATICS, APPLIED Journal of Nonlinear Mathematical Physics Pub Date : 2024-06-10 DOI:10.1007/s44198-024-00203-2
Vladimir L. Kalashnikov, Alexander Rudenkov, Evgeni Sorokin, Irina T. Sorokina
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Abstract

We present the adiabatic theory of dissipative solitons (DS) of complex cubic-quintic nonlinear Ginzburg–Landau equation (CQGLE). Solutions in the closed analytical form in the spectral domain have the shape of Rayleigh–Jeans distribution for a positive (normal) dispersion. The DS parametric space forms a two-dimensional (or three-dimensional for the complex quintic nonlinearity) master diagram connecting the DS energy and a universal parameter formed by the ratio of four real and imaginary coefficients for dissipative and non-dissipative terms in CQGLE. The concept of dissipative soliton resonance (DSR) is formulated in terms of the master diagram, and the main signatures of transition to DSR are demonstrated and experimentally verified. We show a close analogy between DS and incoherent (semicoherent) solitons with an ensemble of quasi-particles confined by a collective potential. It allows applying the thermodynamical approach to DS and deriving the conditions for the DS energy scalability.

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耗散孤子共振:绝热理论与热力学
我们提出了复立方-五次方非线性金兹堡-朗道方程(CQGLE)的耗散孤子(DS)绝热理论。频谱域中封闭解析形式的解在正(正)色散情况下具有雷利-让斯分布(Rayleigh-Jeans distribution)的形状。DS 参数空间形成一个二维(或复五次非线性的三维)主图,连接 DS 能量和一个通用参数,该参数由 CQGLE 中耗散项和非耗散项的四个实系数和虚系数之比形成。根据主图提出了耗散孤子共振(DSR)的概念,并演示和实验验证了向 DSR 过渡的主要特征。我们展示了耗散孤子与非相干(半相干)孤子之间的密切类比关系,以及由集体势能限制的准粒子集合。这使得我们可以将热力学方法应用于 DS,并推导出 DS 能量可扩展性的条件。
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来源期刊
Journal of Nonlinear Mathematical Physics
Journal of Nonlinear Mathematical Physics PHYSICS, MATHEMATICAL-PHYSICS, MATHEMATICAL
CiteScore
1.60
自引率
0.00%
发文量
67
审稿时长
3 months
期刊介绍: Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles. Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics. The main subjects are: -Nonlinear Equations of Mathematical Physics- Quantum Algebras and Integrability- Discrete Integrable Systems and Discrete Geometry- Applications of Lie Group Theory and Lie Algebras- Non-Commutative Geometry- Super Geometry and Super Integrable System- Integrability and Nonintegrability, Painleve Analysis- Inverse Scattering Method- Geometry of Soliton Equations and Applications of Twistor Theory- Classical and Quantum Many Body Problems- Deformation and Geometric Quantization- Instanton, Monopoles and Gauge Theory- Differential Geometry and Mathematical Physics
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