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Solitons and the Inverse Scattering Transform

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First unchanging 'soliton' wave found in space

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Abstract We consider behaviour of sonic-Langmuir solitons which are Langmuir oscillations trapped in regions of reduced plasma density caused by the ponderomotive force due to a high-frequency field. Thornhill and D. Search ADS.

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See the examples in the pictures below. It is interesting that such things exist at all. People once doubted their existence. However, the mathematical theory of solitons is now a well developed "science".

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Solitons have practical applications and they are also interesting subjects of theoretical study. Four interesting and surprising things about solitons are: Integrability : Before the discovery of solitons, mathematicians and people who used math were under the impression that we could not solve nonlinear partial differential equations However, solitons led us to recognize that through a combination of such diverse subjects as quantum physics and algebraic geometry, we can actually solve some nonlinear equations exactly, which gives us a tremendous "window" into what is possible in nonlinearity.

Soliton - Scholarpedia

Nonlinear Superposition : In linear equations there is a simple way to make new solutions from known ones, just multiply them by scalars and add! ScienceDaily, 31 July Laser solitons: Theory, topology and potential applications. Retrieved September 22, from www. With these fibers, they also provided experimental In a new paper, a team of mathematicians, physicists and engineers tackles a famous, year-old problem tied to these Below are relevant articles that may interest you. ScienceDaily shares links with scholarly publications in the TrendMD network and earns revenue from third-party advertisers, where indicated.

An Explicit Example: The KdV 2-Soliton Collision

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