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From weak discontinuities to nondissipative shock waves

  • Statistical, Nonlinear, and Soft Matter Physics
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Abstract

An analysis is presented of the effect of weak dispersion on transitions from weak to strong discontinuities in inviscid fluid dynamics. In the neighborhoods of transition points, this effect is described by simultaneous solutions to the Korteweg—de Vries equation u ′ t + uu ″ x + u ‴ xxx = 0 and fifth-order nonautonomous ordinary differential equations. As x2 + t 2 →∞, the asymptotic behavior of these simultaneous solutions in the zone of undamped oscillations is given by quasi-simple wave solutions to Whitham equations of the form r i(t, x) = tli x/t2.

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450008, Bashkortostan, Russia

    R. N. Garifullin & B. I. Suleimanov

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  1. R. N. Garifullin
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  2. B. I. Suleimanov
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Correspondence to R. N. Garifullin.

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Original Russian Text © R.N. Garifullin, B.I. Suleimanov, 2010, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ-Fiziki, 2010, Vol. 137, No. 1, pp. 149–164.

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Garifullin, R.N., Suleimanov, B.I. From weak discontinuities to nondissipative shock waves. J. Exp. Theor. Phys. 110, 133–146 (2010). https://doi.org/10.1134/S1063776110010164

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  • DOI: https://doi.org/10.1134/S1063776110010164

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