Extended models of nonlinear waves in liquid with gas bubbles
arXiv:1610.04539 · doi:10.1016/j.ijnonlinmec.2014.03.011
Abstract
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
References in corpus (9)
- Simplest equation method to look for exact solutions of nonlinear differential equations
- On asymptotically equivalent shallow water wave equations
- Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer
- Equation for three-dimensional nonlinear waves in liquid with gas bubbles
- Wave interactions and the analysis of the perturbed Burgers equation
- Extended equation for description of nonlinear waves in liquid with gas bubbles
- Exact solutions of equations for the Burgers hierarchy
- Linearizability of the Perturbed Burgers Equation
- Evolution equation for bidirectional surface waves in a convecting fluid
Cited by in corpus (7)
- Dust-acoustic solitary waves in a magnetized dusty plasma with nonthermal electrons and trapped ions
- Special solutions of high order equation for waves in liquid with gas bubbles
- Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture
- Periodic structures described by the perturbed Burgers-Korteweg-de Vries equation
- Analytical and numerical studying of the perturbed Korteweg--de Vries equation
- Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: Further development of methodology with two applications
- Nonlinear Dynamics of a Viscous Bubbly Fluid