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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Citation
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