A different approach for soliton solution of the improved Boussinesq equation

International Journal of Computer Mathematics

Volumn 81, Issue 3, 2004, Pages 313-323

  Inc, M ^a   Evans, D J ^b  

^a FIRAT UNIVERSITY   (Turkey)

^b NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

Author keywords

Adomian decomposition method; Adomian polynomials; The improved Boussinesq equation

Indexed keywords

SOLITONS;

ADOMIAN DECOMPOSITION METHOD; ADOMIAN POLYNOMIALS; THE IMPROVED BOUSSINESQUE EQUATION;

CONVERGENCE OF NUMERICAL METHODS;

EID: 26844555700     PISSN: 00207160     EISSN: 10290265     Source Type: Journal    
DOI: 10.1080/00207160310001650053     Document Type: Article

References (24)

1. Boussinesq, J. (1871). Théorie de I'intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal rectangulaire. Comptes Rendus, 72, 755-759.
2. Kaya, D. (2001). Explicit solutions of generalized nonlinear Boussinesq equation. J. Appl. Math., 1(1), 29-37.
3. Rosenau, P. (1987). Dynamics of dense lattices. Phys. Rev. B, 36(3), 5868-5876.
4. Debnath, L. (1998). Nonlinear PDEs for Scientists and Engineers. Birkhäuser, Boston.
5. Bratsos, A. G. (1998). The solution of the Boussinesq equation using the method of lines. Comput. Methods Appl. Mech. Eng., 157, 33-44.
6. Defrutos, J., Ortega, T. and Sanz-Serna, J. M. (1991). Pseudospectral method for the 'good' Boussinesq equation. Math. Comp., 57, 109-122.
7. Ortega, T. and Sanz-Serna, J. M. (1990). Nonlinear stability and convergence of finite-difference methods for the 'good' Boussinesq equation. Num. Math., 58, 215-229.
8. Manoranjan, V. S., Mitchell, A. R. and Morris, J. L. (1984). Numerical solutions of the 'good' Boussinesq equation. SIAM J. Sci. Stat. Comp., 5, 946-957.
9. Pani, A. K. and Saranga, H. (1997). Finite element Galerkin method for 'good' Boussinesq equation. Nonlinear Analysis, 29(8), 937-956.
10. Wazwaz, A. M. (2001). Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method. Chaos, Solitons and Fractals, 12, 1549-1556.
11. Yan, Z. (2002). New families of solitons with compact support for Boussinesq-like B(m, n) equations with fully nonlinear dispersion. Chaos, Solitons and Fractals, 14, 1151-1158.
12. Iskandar, L. and Jain, P. C. (1980). Numerical solutions of the improved Boussinesq equation. Proc. Indian Acad. Sci., 89, 171-181.
13. Bogolubsky, I. L. (1997). Some examples of inelastic soliton interaction. Comput. Phys. Commun., 13, 149-155.
14. Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Press, Boston.
15. Adomian, G. (1989). A review of the decomposition method and some recent results for nonlinear equations. Comput. Math. Appl., 21, 101-127.
16. Wazwaz, A. M. and Khuri, S. A. (1996). A reliable technique for solving the weakly singular second-kind Volterra-type integral equations. Appl. Math. Comput., 80, 287-299.
17. Wazwaz, A. M. (2000). An approximate solution to boundary-value problems of higher order by the modified decomposition method. Comput. Math. Applic., 40, 679-691.
18. Wazwaz, A. M. (1995). On the solution of the fourth order parabolic equations by the decomposition method. Intern. J. Computer Math., 57, 213-217.
19. Cherruault, Y. (1989). Convergence of Adomian's method. Kybernetes, 18(2), 31-38.
20. Cherruault, Y. and Adomian, G. (1993). Decomposition method: A new proof of convergence. Math. Comput. Modelling, 18(12), 103-106.
21. Abbaoui, K., Pujol, M. J., Cherruault, Y., Himoun, N. and Grimait, P. (2001). A new formulation of Adomian method, convergence result. Kybernetes, 30(9/10), 1183-1191.
22. Ngarhasta, N., Some, B., Abbaoui, K. and Cherruault, Y. (2002). New numerical study of Adomian method applied to a diffusion model. Kybernetes, 31(1), 61-75.
23. Mavoungou, T. and Cherruault, Y. (1992). Convergence of Adomian's method and applications to nonlinear partial differential equations. Kybernetes, 21(6), 13-25.
24. El-Zoheiry, H. (2002) Numerical study of the improved Boussinesq equation. Chaos, Solitons and Fractals, 14, 377-384.