Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method

Applied Mathematics E - Notes

Volumn 5, Issue , 2005, Pages 89-96

  Inc, Mustafa ^b   Ergüt, Mahmut ^a  

^a FIRAT UNIVERSITY   (Turkey)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 14744304129     PISSN: 16072510     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (23)

1. M. L. Wang, Solitary wave solutions for variant Boussinesq equation, Phys. Lett. A, 199(1995), 169-172.
2. L. Yang, J. Liu and K. Yang, Exact solutions of nonlinear PDE, nonlinear transformations and reduction of nonlinear PDE to a quadrature, Phys. Lett. A, 278(2001), 267-270.
3. N. A. Kudryashov, Exact solutions of the generalized Kuramoto-Sivashinsky equation, Phys. Lett. A, 147(1990), 287-291.
4. W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60(1992), 650-654.
5. M. Inc, Travelling and periodic wave solutions of a classical Boussinesq system, Soochow J. Math., 30(2004), 91-102.
6. M. J. Ablowitz and P. A. Clarkson, Soliton: Nonlinear Evolution Equations and Inverse Scattering, Cambridge University Press, Cambridge, 1991.
7. M. R. Miura, Bäcklund Transformation, Springer-Verlag, Berlin, 1978.
8. R. Hirota and J. Satsuma, Soliton solutions of a coupled Korteweg-de Vries equation, Phys. Lett. A, 85(1981), 407-408.
9. Z. Yan and H. Q. Zhang, New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water, Phys. Lett. A, 285(2001), 355-362.
10. A. V. Porubov, Periodical solution to the nonlinear dissipative equation for surface waves in a convecting liquid layer, Phys. Lett. A, 221(1996), 391-394.
11. K. W. Chow, A class of exact, periodic solutions of nonlinear envelope equations, J. Math. Phys., 36(1995), 4125-4137.
12. Z. Yan and H. Q. Zhang, New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics, Phys. Lett. A, 252(1999), 291-296.
13. M. Inc and D. J. Evans, On travelling wave solutions of some nonlinear evolution equations, Intern. J. Computer Math. 81(2004), 191-202.
14. E. G. Fan, Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method, J. Phys. A, 35(2002), 6853-6872.
15. G. B. Whitham, Linear and Nonlinear Waves, New York: Wiley, 1974.
16. J. Hietarinta, Partially Integrable Evolution Equations in Physics, Dordrecht: Kluwer, 1990.
17. R. Hirota, Solitons, Springer: Berlin, 1980.
18. Y. T. Gao and B. Tian, Generalized tanh method with symbolic computation and generalized shallow water wave equation, Computers Math. Applic., 33(1997), 115-118.
19. Z. Yan and H. Q. Zhang, Constructing families of soliton-like solutions to a (2+1)-dimensional breaking soliton equation using symbolic computation, Computers Math. Applic., 44(2002), 1439-1444.
20. S. A. Elwakil, S. K. El-labany, M. A. Zahran and R. Sabry, Exact travelling wave solutions for the generalized shallow water wave equation, Chaos, Solitons and Fractals, 17(2003), 121-126.
21. H. Chen and H. Q. Zhang, Improved jacobi elliptic function method and its applications, Chaos, Solitons and Fractals, 15(2003), 585-591.
22. P. A. Clarksonz and E. L. Mansfield, Symmetry reductions and exact solutions of a class of nonlinear heat equations, Physica D, 70(1993), 250-288.
23. E. G. Fan, Travelling wave solutions for two generalized Hirota-Satsuma KdV systems, Z. Naturforsch, 56(2001), 312-318.