Riemann’s Wavesin Chaplygin Gas

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Abstract


We have investigated propagation of Riemann waves in an ideal fluid with negative pressure, the so-called Chaplygin gas. We consider barotropic motion of the medium when the pressure is P = P( ρ) in the assumption u = u( ρ), where u — the velocity, ρ — density of the medium. The system of hydrodynamic equations then reduces to a wave equation of the first order, which describes a wave with variable speed. It is shown that these waves have deformed profile, which leads to an ambiguous definition of ρ. In order to remove this lack in the original equation we have introduced a member with the second derivative, which leads to the appearance of waves with a stationary profile which is a rarefaction wave.

About the authors

M B Vilca Chaicha

Peoples’ Friendship University of Russia

Department of Theoretical Physics

Yu P Rybakov

Peoples’ Friendship University of Russia

Email: soliton4@mail.ru
Department of Theoretical Physics

G N Shikin

Peoples’ Friendship University of Russia

Department of Theoretical Physics

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Copyright (c) 2012 Вилка Чайча М.Б., Рыбаков Ю.П., Шикин Г.Н.

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