Application of variational iteration method and homotopy perturbation method to the modified Kawahara equation

Mathematical and Computer Modelling

Volumn 49, Issue 3-4, 2009, Pages 573-578

  Jin, Lin ^a  

^a ZHEJIANG GONGSHANG UNIVERSITY   (China)

Author keywords

Approximate solution; Exact solution; Homotopy perturbation method; Modified Kawahara equation; Variational iteration method

Indexed keywords

ITERATIVE METHODS; NUMERICAL METHODS; OSCILLATORS (MECHANICAL); PARTICLE SIZE ANALYSIS;

APPROXIMATE SOLUTION; EXACT SOLUTION; HOMOTOPY PERTURBATION METHOD; MODIFIED KAWAHARA EQUATION; VARIATIONAL ITERATION METHOD;

PERTURBATION TECHNIQUES;

EID: 58049180109     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2008.06.017     Document Type: Article

References (25)

1. Sirendaoreji. New exact travelling wave solutions for the Kawahara and modified Kawahara equations. Chaos Solitons Fractals 19 (2004) 147-150
2. Berloff N.G., and Howard L.N. Solitary and periodic solutions to nonlinear nonintegrable equations. Stud. Appl. Math. 99 (1997) 1-24
3. Bridges T., and Derks G. Linear instability of solitary wave solutions of the Kawahara equation and its generalizations. SIAM. J. Math. Anal. 33 6 (2002) 1356-1378
4. Hunter J.K., and Scheurle J. Existence of perturbed solitary wave solutions to a model equation for water waves. Physica D 32 (1998) 253-268
5. Kawahara T. Oscillatory solitary waves in dispersive media. J. Phys. Soc. Japan 33 (1972) 260-264
6. Fu Z.T., Liu S.K., Liu S.D., and Zhao Q. The JEFE method and periodic solutions of two kinds of nonlinear wave equations. Commun. Nonlinear Sci. Numer. Simul. 8 (2003) 67-75
7. Kaya D., and Al-Khaled K. A numerical comparison of a Kawahara equation. Phys. Lett. A 363 5-6 (2007) 433-439
8. Polat N., Kaya D., and Tutalar H.I. An analytic and numerical solution to a modified Kawahara equation and a convergence analysis of the method. Appl. Math. Comput. 179 (2006) 466-472
9. Wazwaz A.M. New solitary wave solutions to the Kuramoto-Sivashinsky and the Kawahara equations. Appl. Math. Comput. 182 2 (2006) 1642-1650
10. Wazwaz A.M. New solitary wave solutions to the modified Kawahara equation. Phys. Lett. A 8 4-5 (2007) 588-592
11. Yusufoǧlu E., Bekir A., and Alp M. Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine-Cosine method. Chaos Solitons Fractals (2006) 10.1016/j.chaos.2006.10.012
12. Zhang D. Doubly periodic solutions of the modified Kawahara equation. Chaos Solitons Fractals 25 (2005) 1155-1160
13. He J.H. Variational iteration method for delay differential equations. Commun. Nonlinear Sci. Numer. Simul. 2 4 (1997) 235-236
14. He J.H. Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput. Methods Appl. Mech. Eng. 167 1-2 (1998) 69-73
15. He J.H. Homotopy perturbation method: A new nonlinear analytical technique. Appl. Math. Comput. 135 (2003) 73-79
16. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Internat. J. Non-Linear Mech. 35 1 (2000) 37-43
17. He J.H. Variational iteration method - a kind of non-linear analytical technique: Some examples. Internat. J. Non-linear Mech. 34 (1999) 699-708
18. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 2-3 (2000) 115-123
19. He J.H., and XH W. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitons Fractals 29 1 (2006) 108-113
20. He J.H. Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B 20 (2006) 1141-1199
21. He J.H. Non-Perturbative Methods for Strongly Nonlinear Problems (2006), de-Verlag im Internet GmbH, Berlin dissertation
22. Lu J.F. Variational iteration method for solving two-point boundary value problems. J. Comput. Appl. Math. 207 1 (2007) 92-95
23. Lu J.F. Variational iteration method for solving a nonlinear system of second-order boundary value problems. Comput. Math. Appl. 54 (2007) 1133-1138
24. Lu J.F. He's variational iteration method for the modified equal width equation. Chaos Solitons Fractals (2007) 10.1016/j.chaos.2007.06.104
25. Liao S.J. An approximate solution technique not depending on small parameters: A special example. Internat. J. Non-Linear Mech. 30 3 (1995) 371-380