Dissipative solitons

Dissipative solitons (DSs) are stable solitary localized structures that arise in nonlinear spatially extended dissipative systems due to mechanisms of self-organization. They can be considered as an extension of the classical soliton concept in conservative systems. An alternative terminology includes autosolitons, spots and pulses.

Apart from aspects similar to the behavior of classical particles like the formation of bound states, DSs exhibit entirely nonclassical behavior – e.g. scattering, generation and annihilation – all without the constraints of energy or momentum conservation. The excitation of internal degrees of freedom may result in a dynamically stabilized intrinsic speed, or periodic oscillations of the shape.

DSs have been experimentally observed for a long time. Helmholtz measured the propagation velocity of nerve pulses in 1850. In 1902, Lehmann found the formation of localized anode spots in long gas-discharge tubes. Nevertheless, the term "soliton" was originally developed in a different context. The starting point was the experimental detection of "solitary water waves" by Russell in 1834. These observations initiated the theoretical work of Rayleigh and Boussinesq around 1870, which finally led to the approximate description of such waves by Korteweg and de Vries in 1895; that description is known today as the (conservative) KdV equation.

On this background the term "soliton" was coined by Zabusky and Kruskal in 1965. These authors investigated certain well localised solitary solutions of the KdV equation and named these objects solitons. Among other things they demonstrated that in 1-dimensional space solitons exist, e.g. in the form of two unidirectionally propagating pulses with different size and speed and exhibiting the remarkable property that number, shape and size are the same before and after collision.

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