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Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, Alexander K. Volkov
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we de…
Analytical and numerical studying of the perturbed Korteweg--de Vries equation
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
The perturbed Korteweg--de Vries equation is considered. This equation is used for the description of one--dimensional viscous gas dynamics, nonlinear waves in a liquid with gas bu…
Extended equation for description of nonlinear waves in liquid with gas bubbles
Nikolai A. Kudryashov, Dmitry I. Sinelshchikov
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlin…
Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation
Nikolai A. Kudryashov
The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New exact solutions of this equation are presented.
Nonlinear evolution equations for describing waves in bubbly liquids with viscosity and heat transfer consideration
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscos…
Exact solutions of the Swift-Hohenberg equation with dispersion
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
The Swift-Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift-Hohenberg equation with dispersion are presented. The classification of these solu…
Meromorphic exact solutions of the generalized Bretherton equation
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, Maria V. Demina
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the g…
Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonli…