## THERMAL SCIENCE

International Scientific Journal

### APPLICATION OF THE KUDRYASOV METHOD WITH CHARACTERISTIC SET ALGORITHM TO SOLVE SOME PARTIAL DIFFERENTIAL EQUATIONS IN FLUID MECHANICS

**ABSTRACT**

In this paper, we pay attention the analytical method named, the Kudryashov method combined with characteristic set algorithm for finding the exact travelling solutions of two non-linear PDE in fluid mechanics, which named surface wave equation and the generalized Kuramoto-Sivashinsky equation. The solution procedure of the Kudryashov method can be reduced to solve a large system of algebraic equations, which is hard to solve, then we use characteristic set algorithm to solve this problem. The obtained results show that the Kudryashov method combined with characteristic set algorithm is effective.

**KEYWORDS**

PAPER SUBMITTED: 2018-05-15

PAPER REVISED: 2018-07-28

PAPER ACCEPTED: 2018-08-27

PUBLISHED ONLINE: 2019-04-14

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**3**, PAGES [1363 - 1370]

- He, J.H., Homotopy perturbation method: a new nonlinear analytical technique, Applied Mathematics and Computation, 135(2003),1,pp.73-79
- He, J.H., Notes on the optimal variational iteration method, Applied Mathematics Letters, 25(2012), 10, pp.1579-1581
- Yang, X.J., et al., Exact travelling wave solutions for the local fractional two-dimensional Burger-type equations, Computers and Mathematics with Applications,73(2017),pp.203-210
- Yang, X.J., et al., A new computational approach for solving nonlinear local fractional PDEs, Journal of Computational and Applied Mathematics,339(2018),pp.285-296
- Yang, X.J., et al., Exact travelling-wave solution for local fractional Boussinesq equation in fractal domain, Fractals,25(2017),4,1740006
- Yang, X.J., et al., On exact traveling-wave solutions for local fractional Korteweg-de Vries equation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(2016),8, 084312.
- Yang, X.J., et al.,Exact travelling wave solutions for local fractional partial differential equations in mathematical physics, Mathematical Methods in Engineering (pp. 175-191). Springer, 2019
- Gao,F., et al., Exact travelling-wave solutions for one-dimensional modified korteweg -de vries equation defined on cantor sets, Fractals, 27 (2019),1, 1940010
- Guo, Y. X., Exponential stability analysis of travelling waves solutions for nonlinear delayed cellular neural networks, Dynamical Systems, 32 (2017),4, pp.490-503
- Mirzazadeh, M., et al.,Dispersive optical solitons by Kudryashov's method,Optik,125 (2014), pp.6874-6880
- Wu,W.T., Mathematics Mechanization, Science Press, Beijing, 2000
- Lou,S.Y., et al., Exact solitary wave solutions of surface waves in a convecting fluids, Commun.Theor.Phys., 32(1999),4,pp.563-566
- Shang, Y.D., Explicit and exact solutions to a generalized Kuramoto-Sivashinsky equation (in Chinese), Journal of Ningxia University(Natural Science Edition),21(2000),1,pp.69-71