## THERMAL SCIENCE

International Scientific Journal

## Authors of this Paper

,

### EXACT SOLUTIONS WITH ARBITRARY FUNCTIONS OF THE (4+1)-DIMENSIONAL FOKAS EQUATION

ABSTRACT
In this paper, the (4+1)-dimensional Fokas equation is solved by the generalized F-expansion method, and new exact solutions with arbitrary functions are obtained. The obtained solutions include Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions. It is shown that the generalized F-expansion method can be used for constructing exact solutions with arbitrary functions of some other high dimensional partial differential equations in fluids.
KEYWORDS
PAPER SUBMITTED: 2018-04-25
PAPER REVISED: 2018-06-23
PAPER ACCEPTED: 2019-08-01
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904403X
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2403 - 2411]
REFERENCES
1. Ablowitz, M. J., Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering, Cam-bridge University Press, Cambridge, Mass., USA, 1991.
2. Gardner, C. S., et al., Method for Solving the Korteweg-de Vries Equation, Physical Review Letters, 19 (1967), 19, pp. 1095-1197
3. He, J.-H., Wu, X. H., Exp-Function Method for Non-Linear Wave Equations, Chaos, Solitons and Frac-tals, 30 (2006), 3, pp. 700-708
4. Zhang, S., et al., Multi-Wave Solutions for a Non-Isospectral KdV-Type Equation with Variable Coeffi-cients, Thermal Science, 16 (2012), 5, pp. 1576-1579
5. Zhang, S., et al., A Direct Algorithm of Exp-Function Method for Non-Linear Evolution Equations in Fluids, Thermal Science, 20, (2016), 3, pp. 881-884
6. Zhou, Y. B., et al., Periodic Wave Solutions to a Coupled KdV Equation with Variable Coefficients, Physics Letters A, 308 (2003), 1, pp. 31-36
7. Liu, S. K.,et al., Jacobi Elliptic Function Expansion Method and Periodic Wave Solutions of Non-Linear Wave Equations, Physics Letters A, 289 (2001), 1-2, pp. 69-74
8. Wang, M. L., Zhou, Y. B. The Periodic Wave Solutions for the Klein-Gordon-Schrodinger Equations, Physics Letters A, 318 (2003), 1, pp. 84-92.
9. Wang, M. L., et al., The Periodic Wave Solutions for Two Systems of Non-Linear Wave Equations, Chinese Physics B, 12 (2003), 12, pp. 1341-1348
10. Zhang, S., New Exact Solutions of the KdV-Burgers-Kuramoto Equation, Physics Letters A, 358 (2006), 5-6, pp. 414-420
11. Wang, D. S., Zhang, H. Q., Further Improved F-Expansion Method and New Exact Solutions of Konopelchenko-Dubrovshy Equation, Chaos, Solitons and Fractals, 25 (2005), 3, pp. 601-610
12. Chen, J., et al., A Generalized F-Expansion Method and its Application in High-Dimensional Nonlinear Evolution Equation, Communications in Theoretical Physics, 44 (2005), 8, pp. 307-310
13. Zhang, S., Further Improved F-Expansion Method and New Exact Solutions of Kadomstev-Petviashvili Equation, Chaos, Solitons and Fractals, 32 (2007), 4, pp. 1375-1383
14. Zhang, S., Xia, T. C., A Generalized F-expansion Method and New Exact Solutions of Konopelchenko-Dubrovsky Equations, Applied Mathematics and Computation, 183 (2006), 3, pp. 1190-1200
15. Zhang, S., et al., Bilinearization and New Multi-Soliton Solutions for the (4+1)-Dimensional Fokas Equation, Pramana-Journal of Physics, 86, (2016), 6, pp. 1259-1267