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Exact solutions of the Kudryashov-Sinelshchikov equation. (English) Zbl 1205.35272

Summary: The Kudryashov-Sinelshchikov equation for describing the pressure waves in liquid with gas bubbles is studied. New exact solutions of this equation are found. Modification of truncated expansion method is used for obtaining exact solution of this equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q35 PDEs in connection with fluid mechanics
35A24 Methods of ordinary differential equations applied to PDEs
35C05 Solutions to PDEs in closed form

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References:

[1] Kudryashov, N. A.; Sinelshchikov, D. I., Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer, Phys. Lett. A, 374, 2011-2016 (2010) · Zbl 1236.76075
[2] Korteweg, D. J.; de Vries, G., On the change of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag., 39, 422-443 (1895) · JFM 26.0881.02
[3] Whitham, V., Linear and Nonlinear Waves (1974), Wiley-Interscience: Wiley-Interscience New-York · Zbl 0373.76001
[4] Nakoryakov, V. E.; Sobolev, V. V.; Shreiber, L. R., Long waves perturbations in a gas-liquid mixture, Fluid Dynam., 7, 763-768 (1972)
[5] Kudryashov, N. A., Exact solitary waves of the Fisher equation, Phys. Lett. A, 342, 99-106 (2005) · Zbl 1222.35054
[6] Weiss, J.; Tabor, M.; Carnevalle, G., The Panleve property for partial differential equations, J. Math. Phys., 24, 522-526 (1983) · Zbl 0514.35083
[7] Kudryashov, N. A., Exact soliton solutions of the generalized evolution equation of wave dynamics, J. Appl. Math. Mech., 52, 361-365 (1988)
[8] Weiss, J., The Panleve property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative, J. Math. Phys., 24, 1405-1413 (1983) · Zbl 0531.35069
[9] Kudryashov, N. A., Exact solutions of the generalized Kuramoto-Sivashinsky equation, Phys. Lett. A, 147, 287-291 (1990)
[10] Kudryashov, N. A., Simpliest equation method to look for exact solutions of nonlinear differential equations, Chaos Soliton. Fract., 24, 1217-1231 (2005) · Zbl 1069.35018
[11] Kudryashov, N. A.; Loguinova, N. B., Extended simpliest equation method for nonlinear differential equations, Appl. Math. Comput., 205, 396-402 (2008) · Zbl 1168.34003
[12] Parkes, E. J.; Duffy, B. R., An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations, Comput. Phys. Commun., 98, 288-300 (1996) · Zbl 0948.76595
[13] Kudryashov, N. A.; Demina, M. V., Polygons of differential equations for finding exact solutions, Chaos Soliton. Fract., 33, 1480-1496 (2007) · Zbl 1133.35084
[14] Clarkson, P. A.; Kruskal, M. D., New similarity reductions of the Boussinesq equation, J. Math. Phys., 30, 2201-2213 (1989) · Zbl 0698.35137
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