ARTICLE
Matrix logarithmic wave equation and multi-channel systems in fluid mechanics
 
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Durban University of Technology, Institute of Systems Science, Durban
Online publish date: 2019-10-15
Publish date: 2019-10-15
Submission date: 2018-12-04
Acceptance date: 2019-04-16
 
Journal of Theoretical and Applied Mechanics 2019;57(4):843–852
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ABSTRACT
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.
 
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