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One important discovery in the twentieth century physics is the natural formation of a coherent or a well-ordered structure in continuous media, in contrary to degradation of the state as predicted earlier from the second law of thermodynamics. Here nonlinearity plays the essential role in its process. The discovery of soliton, a localized stable wave in a nonlinear and dispersive medium and the self-organization of fluid turbulence are of the major examples. A soliton is formed primarily in one-dimensional medium where the dispersion and nonlinearity play the essential role. Here the temporal evolution can be described by an infinite dimensional Hamiltonian system that is integrable. While a self-organization appears in an infinite dimensional non-Hamiltonian (or dissipative) system where more than two conservative quantities exist in the limit of no dissipation. In this manuscript, by showing examples of the optical soliton in dielectric fibers and self-organization of turbulence in a toroidal plasma in a magnetic field, we demonstrate these interesting discoveries. The manuscript is intended to describe these discoveries more on philosophical basis with some sacrifice on mathematical details so that the idea is conveyed to those in the wide area of sciences.

Optical soliton in dielectric fibers and self-organization of turbulence in plasmas in magnetic fields