Download Chemical Oscillations, Wawes & Turbulence by Y. Kuramoto PDF

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By Y. Kuramoto

Классическая монография известного японского физика-теоретика профессора Иошики Курамото (Yoshiki Kuramoto) по теории колебаний и волн в распределённых средах. Имеено на эту книгу обычно ссылаются, когда упоминают "модели Курамото" или "осцилляторы Курамото", одна из первых (если не первая) книг, активно использующих понятие нелинейного фазового осциллятора.

Фрагмент книги:

Под редакцией профессора Германа Хакена (Professor Dr. Dr. h.c. Hermann Haken)

Оглавление:

1. Introduction
Part I: Methods
2. Reductive perturbation method
3. approach to section description I
4. approach to part description II
Part II: Applications
5. Mutual Entrainment
6. Chemical Waves
7. Chemical Turbulence
Appendix
References
Subject Index

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Example text

2. SOLITONS IN PERIODIC HETEROGENEOUS MEDIA 19 are exceptional models, in the sense that any additional term, which takes into regard physical effects that were not included in the basic model, breaks the exact integrability. This circumstance suggest the necessity to investigate solitons in nonintegrable models (in a strict mathematical sense, these solutions are not "solitons", but rather "solitary waves"; however, following commonly adopted practice, they will be called solitons). In many physically relevant situations, the additional terms which break the integrability of the unperturbed model are small, making it natural to apply a perturbation theory relying on an asymptotic expansion around exact solutions provided by the 1ST in the absence of the perturbations.

L 1 L. 10: A typical example of the shape (shown on the logarithmic scale) of dispersion-managed solitons in the ideal lossless model, and in its realistic counterpart with lumped filters and amplifiers (for comparison, the solitons with equal amplitudes are taken in both cases). Each soliton is shown at a position (close to the midpoint of the anomalous-GVD segment of the DM map) where it is narrowest. 45) (the latter is usually referred to as the Gaussian transfer function with the bandpass width Aw).

It is composed of alternating BGs with opposite signs of the Kerr nonlinearity, and also gives rise to a family of robust solitons. A periodic heterogeneous system with the x^^^ nonlinearity was proposed in the form of the so-called tandem model [162], which combines linear segments and ones carrying the quadratic nonlinearity [162]. Specific solitons were revealed by numerical simulations in this model. In all these systems, stable solitons exist in the form of periodically oscillating breathers (obviously, the solitons cannot keep a permanent shape propagating through the inhomogeneous structure).

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