Akhmediev N, Soto-Crespo J M, Vouzas Peter, Devine N, Chang Wonkeun
Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Acton ACT 2601, Australia
Instituto de Óptica, C.S.I.C., Serrano 121, 28006 Madrid, Spain.
Philos Trans A Math Phys Eng Sci. 2018 Jul 28;376(2124). doi: 10.1098/rsta.2018.0023.
Prigogine's ideas of systems far from equilibrium and self-organization (Prigogine & Lefever. 1968 , 1695-1700 (doi:10.1063/1.1668896); Glansdorff & Prigogine. 1971 New York, NY/London, UK: Wiley) deeply influenced physics, and soliton science in particular. These ideas allowed the notion of solitons to be extended from purely integrable cases to the concept of dissipative solitons. The latter are qualitatively different from the solitons in integrable and Hamiltonian systems. The variety in their forms is huge. In this paper, one recent example is considered-dissipative solitons with extreme spikes (DSESs). It was found that DSESs exist in large regions of the parameter space of the complex cubic-quintic Ginzburg-Landau equation. A continuous variation in any of its parameters results in a rich structure of bifurcations.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.
普里戈金关于远离平衡态系统和自组织的思想（普里戈金和勒菲弗，1968年，第1695 - 1700页（doi:10.1063/1.1668896）；格兰斯多夫和普里戈金，1971年，纽约，纽约州/英国伦敦：威利出版社）对物理学，尤其是孤子科学产生了深远影响。这些思想使得孤子的概念从纯粹的可积情形扩展到了耗散孤子的概念。后者在性质上与可积系统和哈密顿系统中的孤子不同。它们的形式种类繁多。在本文中，考虑了一个近期的例子——具有极端尖峰的耗散孤子（DSESs）。研究发现，在复立方 - 五次金兹堡 - 朗道方程参数空间的很大区域内存在DSESs。其任何一个参数的连续变化都会导致丰富的分岔结构。本文是主题为“远离平衡态物质中的耗散结构：从化学、光子学到生物学（第1部分）”的一部分。
