ISSN:
1432-0924
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Abstract A soliton is the wave which propagates in the form of stable bulk with concentrated energy. Zabusky and Kruskal discovered it in 1965 by solving numerically the K-dV equation, and consequently a variety of analytical methods were established for studying its physical property to introduce the new field of modern physics. This paper succeeds in demonstrating computationally interaction of solitons concerning recurrence of the initial state suggested by Zabusky and Kruskal where ambiguity about their numerical analysis has prevented us from obtaining stable solution representing recurrent phenomenon for a long time. Here numerical experiment enables us to examine instability occasioning in the leapfrog method with a function of the initial condition which served as a key parameter. It is clarified that: (i) this finite difference approximation is available to describe only weakly coupled interaction of solitons, (ii) on linear analysis point of view, instability results from increasing unstable numerical mode of the higher Fourier components which was attributed to dispersive property of this difference method and (iii) instability originates in a sharp solitary wave which was standing still at the point of its birth.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01046944
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