Matrix logarithmic wave equation and multi-channel systems in fluid mechanics
arXiv:1906.01816 · doi:10.15632/jtam-pl/112063
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.
6 pages, final version
Cited by in corpus (5)
- An alternative to dark matter and dark energy: Scale-dependent gravity in superfluid vacuum theory
- Resolving the puzzle of sound propagation in liquid helium at low temperatures
- Resolving the puzzle of sound propagation in a dilute Bose-Einstein condensate
- Sound propagation in cigar-shaped Bose liquids in the Thomas-Fermi approximation: A comparative study between Gross-Pitaevskii and logarithmic models
- Acoustic oscillations in cigar-shaped logarithmic Bose-Einstein condensate in the Thomas-Fermi approximation