Multiple-front solutions for the Burgers equation and the coupled Burgers equations

Applied Mathematics and Computation

Volumn 190, Issue 2, 2007, Pages 1198-1206

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Burgers equation; Coupled Burgers equations; Multiple front solutions; tanh coth Method

Indexed keywords

HOPF BIFURCATION; MATHEMATICAL TRANSFORMATIONS;

BURGERS EQUATION; COUPLED BURGERS EQUATIONS; MULTIPLE-FRONT SOLUTIONS; TANH-COTH METHOD;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 34250643151     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.02.003     Document Type: Article

References (22)

1. Burgers J.M. The Nonlinear Diffusion Equation (1974), Reiedl, Dordtrecht
2. Veksler A., and Zarmi Y. Wave interactions and the analysis of the perturbed Burgers equation. Physica D 211 (2005) 57-73
3. Veksler A., and Zarmi Y. Freedom in the expansion and obstacles to integrability in multiple-soliton solutions of the perturbed KdV equation. Physica D 217 (2006) 77-87
4. Ma Z.-Y., Wu X.-F., and Zhu J.-M. Multisoliton excitations for the Kadomtsev-Petviashvili equation and the coupled Burgers equation. Chaos Soliton. Fract. 31 (2007) 648-657
5. Wazwaz A.M. Partial Differential Equations: Methods and Applications (2002), Balkema Publishers, The Netherlands
6. Ma W.X. A hierarchy of coupled Burgers systems possessing a hereditary structure. J. Phys. A: Math. Gen. 26 (1993) 1169-1174
7. Ablowitz M.J., and Segur H. Solitons and Inverse Scattering Transform (1981), SIAM, Philadelphia, PA
8. Hereman W., and Zhaung W. Symbolic software for soliton theory. Acta Appl. Math., Phys. Lett. A 76 (1980) 95-96
9. Hereman W., and Nuseir A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comp. Simul. 43 (1997) 13-27
10. Hirota R. The Direct Method in Soliton Theory (2004), Cambridge University Press, Cambridge
11. Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
12. Hirota R. Exact solutions of the modified Korteweg-de Vries equation for multiple collisions of solitons. J. Phys. Soc. Jpn. 33 5 (1972) 1456-1458
13. Hirota R. Exact solutions of the Sine-Gordon equation for multiple collisions of solitons. J. Phys. Soc. Jpn. 33 5 (1972) 1459-1463
14. Hirota R. Exact N-soliton solutions of a nonlinear wave equation. J. Math. Phys. 14 7 (1973) 805-809
15. Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. I. KdV-type bilinear equations. J. Math. Phys. 28 8 (1987) 1732-1742
16. Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. II. mKdV-type bilinear equations. J. Math. Phys. 28 9 (1987) 2094-2101
17. Hietarinta J. A search for bilinear equations passing Hirota's three-soliton condition. III. Sine-Gordon-type bilinear equations. J. Math. Phys. 28 11 (1987) 2586-2592
18. Malfliet W., and Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys. Scripta 54 (1996) 563-568
19. Malfliet W., and Hereman W. The Tanh Method: II. Perturbation technique for conservative systems. Phys. Scripta 54 (1996) 569-575
20. Wazwaz A.M. The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations. Appl. Math. Comput. 184 2 (2007) 1002-1014
21. A.M. Wazwaz, The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.11.013.
22. Wazwaz A.M. New solitary-wave special solutions with compact support for the nonlinear dispersive K (m, n) equations. Chaos Soliton. Fract. 13 2 (2002) 321-330