Exact solutions for the generalized BBM equation with variable coefficients

Mathematical Problems in Engineering

Volumn 2010, Issue , 2010, Pages

  Salas, Alvaro H ^b,c   Gmez, Cesar A ^a  

^a UNIVERSIDAD NACIONAL DE COLOMBIA   (Colombia)

^b UNIVERSIDAD NACIONAL DE COLOMBIA   (Colombia)

^c UNIVERSIDAD DE CALDAS   (Colombia)

Author keywords

[No Author keywords available]

Indexed keywords

BBM EQUATIONS; BENJAMIN-BONA-MAHONY EQUATIONS; EXACT SOLUTION; EXP-FUNCTION METHOD; ITERATION ALGORITHMS; SOLITON SOLUTIONS; VARIABLE COEFFICIENTS;

SOLITONS;

ALGORITHMS;

EID: 77951432014     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2010/498249     Document Type: Article

References (35)

1. Benjamin T. B., Bona J. L., Mahony J. J., Model equations for long waves in nonlinear dispersive systems Philosophical Transactions of the Royal Society of London. Series A 1972 272 1220 47 78
2. Korteweg D. J., de Vries G., On the change of long waves advancing in a rectangular canal and a new type of long stationary wave Philosophical Magazine 1835 39 422 443
3. Morrison P. J., Meiss J. D., Cary J. R., Scattering of regularized-long-wave solitary waves Physica D 1984 11 3 324 336
4. Miura R. M., Korteweg-de Vries equation and generalizations. I. A remarkable explicit nonlinear transformation Journal of Mathematical Physics 1968 9 1202 1204
5. Nirmala N., Vedan M. J., Baby B. V., Auto-Bcklund transformation, Lax pairs, and Painlev property of a variable coefficient Korteweg-de Vries equation. I Journal of Mathematical Physics 1986 27 11 2640 2643
6. Liu Z., Yang C., The application of bifurcation method to a higher-order KdV equation Journal of Mathematical Analysis and Applications 2002 275 1 1 12
7. Zhang Y., Lai S., Yin J., Wu Y., The application of the auxiliary equation technique to a generalized mKdV equation with variable coefficients Journal of Computational and Applied Mathematics 2009 223 1 75 85
8. He J.-H., Variational iteration method for autonomous ordinary differential systems Applied Mathematics and Computation 2000 114 2-3 115 123
9. He J.-H., Homotopy perturbation method: a new nonlinear analytical technique Applied Mathematics and Computation 2003 135 1 73 79
10. He J.-H., The homotopy perturbation method nonlinear oscillators with discontinuities Applied Mathematics and Computation 2004 151 1 287 292
11. Wazwaz A.-M., The variational iteration method for rational solutions for KdV, K(2,2), Burgers, and cubic Boussinesq equations Journal of Computational and Applied Mathematics 2007 207 1 18 23
12. Yusufoglu E., Bekir A., The variational iteration method for solitary patterns solutions of gBBM equation Physics Letters. A 2007 367 6 461 464
13. Zhu J.-M., Lu Z.-M., Liu Y.-L., Doubly periodic wave solutions of Jaulent-Miodek equations using variational iteration method combined with Jacobian-function method Communications in Theoretical Physics 2008 49 6 1403 1406
14. Gmez C. A., Salas A. H., The variational iteration method combined with improved generalized tanh-coth method applied to Sawada-Kotera equation. Applied Mathematics and Computation, 2009. In press
15. He J.-H., Wu X.-H., Exp-function method for nonlinear wave equations Chaos, Solitons and Fractals 2006 30 3 700 708
16. Zhang S., Exp-function method exactly solving the KdV equation with forcing term Applied Mathematics and Computation 2008 197 1 128 134 (Pubitemid 351215484)
17. He J.-H., Zhang L.-N., Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method Physics Letters. A 2008 372 7 1044 1047
18. Zhang S., Application of Exp-function method to a KdV equation with variable coefficients Physics Letters. A 2007 365 5-6 448 453
19. Salas A. H., Exact solutions for the general fifth KdV equation by the exp function method Applied Mathematics and Computation 2008 205 1 291 297
20. Salas A. H., Gmez C. A., Castillo Hernadez J. E., New abundant solutions for the Burgers equation Computers Mathematics with Applications 2009 58 3 514 520
21. Zhang S., Exp-function method: solitary, periodic and rational wave solutions of nonlinear evolution equations Nonlinear Science Letters A 2010 1 143 146
22. He J.-H., Wu G.-C., Austin F., The variational iteration method which should be followed Nonlinear Science Letters A 2010 1.1 1 30
23. Dai Z.-D., Wang C.-J., Lin S.-Q., Li D.-L., Mu G., The three-wave method for nonlinear evolution equations Nonlinear Science Letters A 2010 1 1 77 82
24. Fu H.-M., Dai Z.-D., Double Exp-function method and application International Journal of Nonlinear Sciences and Numerical Simulation 2009 10 7 927 933
25. Salas A. H., Some solutions for a type of generalized Sawada-Kotera equation Applied Mathematics and Computation 2008 196 2 812 817
26. Salas A. H., Gmez C. A., Computing exact solutions for some fifth KdV equations with forcing term Applied Mathematics and Computation 2008 204 1 257 260
27. Salas A. H., Gmez C. A., Escobar J. G., Exact solutions for the general fifth order KdV equation by the extended tanh method Journal of Mathematical Sciences: Advances and Applications 2008 1 2 305 310
28. Salas A. H., Gmez C. A., A practical approach to solve coupled systems of nonlinear PDE's Journal of Mathematical Sciences: Advances and Applications 2009 3 1 101 107
29. Salas A. H., Gmez C. A, El software Mathematica en la bsqueda de soluciones exactas de ecuaciones diferenciales no lineales en derivadas parciales mediante el uso de la ecuacin de Riccati 1 Memorias del Primer Seminario Internacional de Tecnologas en Educacin Matemtica 2005 Universidad Pedaggica Nacional, Santaf de Bogot, Colombia 379 387
30. Salas A. H., Castillo H. J., Escobar J. G., About the seventh-order Kaup-Kupershmidt equation and its solutions. September 2008, http://arxiv.org, arXiv:0809.2865
31. Salas A. H., Escobar J. G., New solutions for the modified generalized Degasperis-Procesi equation. September 2008, http://arxiv.org/abs/0809.2864
32. Salas A. H., Two standard methods for solving the Ito equation. May 2008, http://arxiv.org/abs/0805.3362
33. Salas A. H., Some exact solutions for the Caudrey-Dodd-Gibbon equation. May 2008, http://arxiv.org/abs/0805.3362
34. Salas S A. H., Gmez S C. A., Exact solutions for a third-order KdV equation with variable coefficients and forcing term Mathematical Problems in Engineering 2009 2009 13
35. Gmez S C. A., Salas A. H., The Cole-Hopf transformation and improved tanh-coth method applied to new integrable system (KdV6) Applied Mathematics and Computation 2008 204 2 957 962