N-soliton solutions for the combined KdV-CDG equation and the KdV-Lax equation

Applied Mathematics and Computation

Volumn 203, Issue 1, 2008, Pages 402-407

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

CDG equation; Hirota bilinear method; Lax equation; N Soliton solutions

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS;

BILINEAR METHODS; BOUNDARY CONDITIONING; CDG EQUATION; HIROTA BILINEAR METHOD; INTEGRABLE EQUATIONS; LAX EQUATION; N-SOLITON SOLUTIONS; ONE-DIMENSION; SOLITON SOLUTIONS;

SOLITONS;

EID: 50249112604     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.04.047     Document Type: Article

References (30)

1. Hirota R., and Ito M. Resonance of solitons in one dimension. J. Phys. Soc. Jpn. 52 3 (1983) 744-748
2. Caudrey P.J., Dodd R.K., and Gibbon J.D. A new heirarchy of Korteweg-de Vries equations. Proc. Roy. Soc. Lond. A 351 (1976) 407-422
3. Lax P.D. Integrals of nonlinear equations of evolurion and solitary waves. Commun. Pure Appl. Math. 21 (1968) 467-490
4. Ablowitz M.J., Kaup D.J., Newell A.C., and Segur H. The Inverse scattering transform-Fourier analysis for nonlinear problems. Stud. Appl. Math. 53 (1974) 249-315
5. Hirota R., and Satsuma J. N-soliton solutions of model equations for shallow water waves. J. Phys. Soc. Jpn. 40 2 (1976) 611-612
6. Hirota R. A new form of Bäcklund transformations and its relation to the inverse scattering problem. Progr. Theor. Phys. 52 5 (1974) 1498-1512
7. Hirota R. The Direct Method in Soliton Theory (2004), Cambridge University Press, Cambridge
8. Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
9. 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
10. 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
11. W. Hereman, W. Zhuang. A MACSYMA program for the Hirota method, in: 13th World Congress on Computation and Applied Mathematics, vol. 2, 1991, pp. 842-863.
12. Hereman W., and Zhuang W. Symbolic computation of solitons with Macsyma. Computat. Appl. Math. II: Differ. Equat. (1992) 287-296
13. W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in: Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, 1991, pp. 22-26.
14. Ito M. An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher order. J. Phys. Soc. Jpn. 49 2 (1980) 771-778
15. Sawada K., and Kotera T. A method for finding N-soliton solutions of the K.d.V. equation and K.d.V.-like equation. Prog. Theor. Phys. 51 (1974) 1355-1367
16. Matsuno Y. Bilinear Transformation Method (1984), Academic Press
17. Malfliet W. The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. J. Computat. Appl. Mathemat. 164-165 (2004) 529-541
18. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 7 (1992) 650-654
19. Malfliet W., and Hereman W. The tanh method. I. Exact solutions of nonlinear evolution and wave equations. Phys. Script. 54 (1996) 563-568
20. Malfliet W., and Hereman W. The tanh method. II. Perturbation technique for conservative systems. Phys. Script. 54 (1996) 569-575
21. Wazwaz A.M. Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method. Appl. Math. Comput. 190 (2007) 633-640
22. Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206
23. Wazwaz A.M. Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method. Appl. Math. Comput. 190 (2007) 633-640
24. Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206
25. Wazwaz A.M. Multiple-soliton solutions for the Boussinesq equation. Appl. Math. Comput. 192 (2007) 479-486
26. Wazwaz A.M. The Hirota's direct method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Ito seventh-order equation. Appl. Math. Comput. 199 (2008) 133-138
27. Wazwaz A.M. Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation. Appl. Math. Comput. 200 (2008) 437-443
28. Wazwaz A.M. Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation. Appl. Math. Comput. 201 (2008) 168-174
29. Wazwaz A.M. The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves. Appl. Math. Comput. 201 1-2 (2008) 489-503
30. Wazwaz A.M. Multiple-soliton solutions of two extended model equations for shallow water waves. Appl. Math. Comput. 201 (2008) 790-799