Abstract
A number of exact and approximate analytical solutions of the equations for one-dimensional and weakly non-one-dimensional waves propagating in a liquid with gas bubbles are presented for the case where the bubble distribution density is a continuous function of the bubble radius and spatial coordinates.
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A. A. Lugovtsov, “Propagation of nonlinear waves in an inhomogeneous gas-liquid medium. Derivation of wave equations in the Korteweg-de Vries approximation,” J. Appl. Mech. Tech. Phys., 50, No. 2, 327–335 (2009).
O. V. Rudenko and S. I. Soluyan, Theoretical Fundamentals of Nonlinear Acoustics [in Russian], Nauka, Moscow (1975).
V. I. Karpman, Nonlinear Waves in Dispersing Media [in Russian], Nauka, Moscow (1973).
S. S. Kutateladze and V. E. Nakoryakov, Heat and Mass Transfer and Waves in Gas-Liquid Systems [in Russian], Nauka, Novosibirsk (1984).
A. A. Lugovtsov and B. A. Lugovtsov, “Investigation of axisymmetric long waves in the Korteweg-de Vries-Burgers approximation,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 1, Inst. of Hydrodynamics, Sib. Div., Russian Acad. of Sci., Novosibirsk (1969), pp. 195–206.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 51, No. 1, pp. 54–61, January–February, 2010.
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Lugovtsov, A.A. Propagation of nonlinear waves in a gas-liquid medium. Exact and approximate analytical solutions of wave equations. J Appl Mech Tech Phy 51, 44–50 (2010). https://doi.org/10.1007/s10808-010-0007-0
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DOI: https://doi.org/10.1007/s10808-010-0007-0