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

Zloshchastiev Konstantin G.

Journal of Theoretical and Applied Mechanics

2019

Vol. 57 nr 4

843--852

We formulate the mapping between a large class of nonlinear wave equations and flow equations for a 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.