## THERMAL SCIENCE

International Scientific Journal

### IMPROVED HYPERBOLIC FUNCTION METHOD AND EXACT SOLUTIONS FOR VARIABLE COEFFICIENT BENJAMIN-BONA-MAHONY-BURGERS EQUATION

**ABSTRACT**

By using the improved hyperbolic function method, we investigate the variable
coefficient Benjamin-Bona-Mahony-Burgers equation which is very important in
fluid mechanics. Some exact solutions are obtained. Under some conditions, the periodic wave leads to the kink-like wave.

**KEYWORDS**

PAPER SUBMITTED: 2015-01-05

PAPER REVISED: 2015-02-27

PAPER ACCEPTED: 2015-03-31

PUBLISHED ONLINE: 2015-10-25

**THERMAL SCIENCE** YEAR

**2015**, VOLUME

**19**, ISSUE

**4**, PAGES [1183 - 1187]

- Zhang, P., Lin, F. H., Lectures on the Analysis of Non-Linear Partial Differential Equations, Higher Education Press, Beijing, China, 2013
- Bona, J. L., Smith, R., The Initial-Value Problem for the Korteweg-de Vries Equation, Philosophical Transactions of the Royal Society of London Series A, 278 (1975), 1287, pp. 555-601
- Benjamin, T. B., et al., Model Equations for Long Waves in Non-Linear Dispersive Systems, Philosophical Transactions of the Royal Society of London Series A, 272 (1972), 1220, pp. 47-78
- Peregrine, D. H., Calculations of the Development of an Under Bore, Journal of Fluid Mechanics, 25 (1966), 2, pp. 321-326
- Mei, M., Large-Time Behavior of Solution for Generalized Benjamin-Bona-Mahony-Burgers Equations, Non-Linear Analysis, 33 (1998), 7, pp. 699-714
- Kumar, V., et al., Painleve Analysis, Lie Symmetries and Exact Solutions for Variable Coefficients Benjamin- Bona-Mahony-Burger (BBMB) Equation, Communications in Theoretical Physics, 60 (2013), 2, pp. 175-182
- Tari, H., Ganji, D. D., Approximate Explicit Solutions of Non-Linear BBMB Equation by He's Methods and Comparison with the Exact Solution, Physics Letters A, 367 (2007), 1, pp. 95-101
- Kadri, T., et al., Methods for the Numerical Solution of the Benjamin-Bona-Mahony-Burgers Equation, Numer. Math. Partial. Diff. Eq., 24 (2008), 6, pp. 1501-1516
- Shi, Y., et al., Exact Solutions of Generalized Burgers' Equation with Variable Coefficients, East China Normal University Transaction, 5 (2006), pp. 27-34
- Shi, Y. R., et al., Exact Solutions of Variable Coefficients Burgers' Equations, Journal of Lanzhou University (Natural Sciences), 41 (2005), 2, pp. 107-112
- Wang, M., et al., Application of a Homogeneous Balance Method to Exact Solutions of Non-Linear Equations in Mathematical Physics, Physics Letters A, 216 (1996), 1, pp. 67-75