Copy herein is from the Website: http://www.tuchemnitz.de/physik/KSND/abb/node6.html: Technische Universität Chemnitz Author: Abdelhadi Benabdallah Email: benabdallah@physik.tuchemnitz.de 

Nonlinear waves: SolitonsSolitons are nonlinear waves. As a preliminary definition, a soliton is considered as solitary, traveling wave pulse solution of nonlinear partial differential equation (PDE). The nonlinearity will play a significant role. For most dispersive evolution equations these solitary waves would scatter inelastically and lose 'energy' due to the radiation. Not so for the solitons: after a fully nonlinear interaction, the solitary waves remerge, retaining their identities with same speed and shape. It should have remarkable stability properties. Stability plays a important role in soliton physics.The beginning of soliton physics in often dated back to the month of August
1834 when John Scott Russell observed the "great wave of translation''. He
describes what he saw in [1]:
Due to the work of Stokes, Boussinesq, Rayleigh, Korteweg, de Vries, and many others we know that the "great wave of translation'' is a special form of a surface water wave. The equation describing the (unidirectional) propagation of waves on the surface of a shallow channel was derived by Korteweg and de Vries in 1895. After performing a Galilean and variety of scaling transformations, the KdV equation can be written in simplified form:
The KdV equation can admits also a Multisoliton solution. [1] J. Scott Russell. Report on waves, Fourteenth meeting of the British Association for the Advancement of Science, 1844.





There is one Universe.
It is perpetual, in equilibrium; and, a manifestation of the . . . Unified Concept;
also,
are a single discipline, which proclaims the
perpetuity and nexus of Life; such is
. . . Conceptualism.
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