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Matrix logarithmic wave equation and multi-channel systems in fluid mechanics

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Polish Society of Theoretical and Applied Mechanics

Abstract

We formulate the mapping between a large class of nonlinear wave equations and flow equations for barotropic fluid with internal surface tension and capillary effects. Motivated by statistical mechanics and multi-channel physics arguments, we focus on wave equations with logarithmic nonlinearity, and further generalize them to matrix equations. We map the resulting equation to flow equations of multi-channel or multi-component Korteweg-type materials. For some special cases, we analytically derive Gaussian-type matrix solutions and study them in the context of fluid mechanics.

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Zloshchastiev, K.G. 2019. Matrix logarithmic wave equation and multi-channel systems in fluid mechanics. Journal of Theoretical and Applied Mechanics. 57(4): 843-852. doi:10.15632/jtam-pl/112063

DOI

10.15632/jtam-pl/112063