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Solitons: Historical and Physical Introduction

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Encyclopedia of Complexity and Systems Science

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The interest in nonlinear physics has grown significantly over the last 50 years. Although numerous nonlinear processes had been previously identified, the mathematic tools of nonlinear physics had not yet been developed. The available tools were linear, and nonlinearities were avoided or treated as perturbations of linear theories. The solitary water wave, experimentally discovered in 1834 by John Scott Russell, led to numerous discussions. This hump-shape localized wave that propagates along one space direction with undeformed shape has spectacular stability properties. John Scott Russell carried out many experiments to obtain the properties of this wave. The theories which were based on linear approaches concluded that this kind of wave could not exist. The controversy was resolved by J. Boussinesq (1871) and by Lord Rayleigh (1876) who showed that if dissipation is neglected, the increase in local wave velocity associated with finite amplitude is balanced...

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  1. Laboratoire Ondes et Milieux Complexes, Fre CNRS 3102, Le Havre, Cedex, France

    François Marin

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    Robert A. Meyers

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Marin, F. (2017). Solitons: Historical and Physical Introduction. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27737-5_506-2

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