Exact solitary solutions for variants of the KdV equations with fractional time derivatives

Chaos, Solitons and Fractals

Volumn 40, Issue 3, 2009, Pages 1264-1270

  Odibat, Zaid M ^a  

^a AL BALQA APPLIED UNIVERSITY   (Jordan)

Author keywords

[No Author keywords available]

Indexed keywords

PERTURBATION TECHNIQUES;

COMPUTABLE COMPONENTS; CONVERGENT SERIES; HOMOTOPY PERTURBATION METHOD (HPM); INITIAL SOLUTION; NONLINEAR PROBLEMS; PHYSICAL STRUCTURES; SOLITARY SOLUTIONS; TIME DERIVATIVE;

KORTEWEG-DE VRIES EQUATION;

EID: 65349119364     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.08.080     Document Type: Article

References (41)

1. Wadati M. Introduction to solitons. Pramana-J Phys 57 5-6 (2001) 841-847
2. Rosenau P., and Hyman J.M. Compactons: solitons with finite wavelengths. Phy Rev Lett 70 5 (1993) 564-567
3. Olver P.J., and Rosenau P. Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support. Phy Rev E 53 2 (1996) 1900-1906
4. Ismail M., and Taha T. A numerical study of compactons. Math Comput Simulat 74 (1998) 519-530
5. Wazwaz A.M. Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Chaos, Solitons & Fractals 12 8 (2001) 1549-1556
6. He J.H., and Wu X. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons & Fractals 29 (2006) 108-113
7. Wazwaz A.M. The tanh-coth method for new compactons and solitons solutions for the K(n, n) and the K(n + 1, n + 1) equations. Appl Math Comput 188 2 (2007) 1930-1940
8. Wazwaz A.M. New sets of solitary wave solutions to the KdV, mKdV and the generalized KdV equations. Commun Nonlin Sci Numer Simulat 13 2 (2008) 331-339
9. Wazwaz A.M. Compact and non-compact solutions for nonlinear dispersive variants of the generalized KdV equation. Appl Math Comput 159 (2004) 577-588
10. Wazwaz A.M., and Helal M. Nonlinear variants of the BBM equation with compact and noncompact physical structures. Chaos, Solitons & Fractals 26 3 (2005) 767-776
11. Wazwaz A.M. The sine-cosine method for obtaining solutions with compact and noncompact structures. Appl Math Comput 159 (2004) 559-576
12. Wazwaz A.M. The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation. Appl Math Comput 167 (2005) 1179-1195
13. Wazwaz A.M. The sine-cosine and the tanh methods: reliable tools for analytic treatment of nonlinear dispersive equations. Appl Math Comput 173 (2006) 150-164
14. Wazwaz A.M. A study of nonlinear dispersive equations with solitary-wave solutions having compact support. Math Comput Simulat 56 (2001) 269-276
15. Wazwaz A.M. Compactons and solitary patterns structures for variants of the KdV and KP equations. Appl Math Comput 139 1 (2003) 37-54
16. Zhu Y., and Chang Q. Exact special solitary solutions with compact support for the nonlinear dispersive K(m, n) equations. Chaos, Solitons & Fractals 27 2 (2006) 487-493
17. Miller K.S., and Ross B. An introduction to the fractional calculus and fractional differential equations (1993), Wiley, New York
18. Podlubny I. Fractional differential equations (1999), Academic Press, San Diego (CA)
19. Momani S., and Odibat Z. Numerical comparison of methods for solving linear differential equations of fractional order. Chaos, Solitons & Fractals 31 5 (2007) 1248-1255
20. Momani S., and Odibat Z. Analytical approach to linear fractional partial differential equations arising in fluid mechanics. Phys Lett A 355 4 (2006) 271-279
21. Odibat Z., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int J Non-linear Sci Numer Simulat 1 7 (2006) 15-27
22. Erturk V, Momani S, Odibat Z. Application of generalized differential transform method to multi-order fractional differential equations. Commun Nonlin Sci Numer Simulat [in press].
23. He J.H. Homotopy perturbation technique. Comput Methods Appl Mech Eng 178 (1999) 257-262
24. He J.H. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J Non-linear Mech 35 1 (2000) 37-43
25. El-Shahed M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. Int J Non-linear Sci Mumer Simulat 6 2 (2005) 163-168
26. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 151 (2004) 287-292
27. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int J Non-linear Sci Mumer Simulat 6 2 (2005) 207-208
28. He J.H. Periodic solutions and bifurcations of delay-differential equations. Phys Lett A 374 4-6 (2005) 228-230
29. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals 26 3 (2005) 695-700
30. He J.H. Homotopy perturbation method for solving boundary value problems. Phys Lett A 350 1-2 (2006) 87-88
31. Odibat Z., and Momani S. Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order. Chaos Solitons & Fractals 36 1 (2008) 167-174
32. He J.H. Homotopy perturbation method: a new nonlinear analytic technique. Appl Math Comput 135 (2003) 73-79
33. He J.H. Comparsion of homotopy perturbation method and homotopy analysis method. Appl Math Comput 156 (2004) 527-539
34. He J.H. Asymptotology by homotopy perturbation method. Appl Math Comput 156 (2004) 591-596
35. He J.H. Limit cycle and bifuraction of nonlinear problems. Chaos, Solitons & Fractals 26 3 (2005) 827-833
36. Siddiqui A., Mahmood R., and Ghori Q. Thin film flow of a third grade fluid on moving a belt by He's homotopy perturbation method. Int J Non-linear Sci Mumer Simulat 7 1 (2006) 7-14
37. He J.H. Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B 20 10 (2006) 1141-1199
38. Abbasbandy S. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method. Appl Math Comput 172 (2006) 485-490
39. Odibat Z., and Momani S. Numerical methods for nonlinear partial differential equations of fractional order. Appl Math Model 32 1 (2008) 28-39
40. Odibat Z. A new modification of the homotopy perturbation method for linear and nonlinear operators. Appl Math Comput 189 1 (2007) 746-753
41. Caputo M. Linear models of dissipation whose Q is almost frequency independent. Part II. J Roy Astr Soc 13 (1967) 529-539