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Abstract: The numerical simulation of compactons, solitary waves with compact support,is characterized by the presence of spurious phenomena, as numerically-inducedradiation, which is illustrated here using four numerical methods applied tothe Rosenau-Hyman Kp,p equation. Both forward and backward radiations areemitted from the compacton presenting a self-similar shape which has beenillustrated graphically by the proper scaling. A grid refinement study showsthat the amplitude of the radiations decreases as the grid size does,confirming its numerical origin. The front velocity and the amplitude of bothradiations have been studied as a function of both the compacton and thenumerical parameters. The amplitude of the radiations decreases exponentiallyin time, being characterized by a nearly constant scaling exponent. An ansatzfor both the backward and forward radiations corresponding to a self-similarfunction characterized by the scaling exponent is suggested by the presentnumerical results.



Autor: Francisco Rus, Francisco R. Villatoro

Fuente: https://arxiv.org/







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