The Cole-Hopf transformation and multiple soliton solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota equation

Applied Mathematics and Computation

Volumn 207, Issue 1, 2009, Pages 248-255

  Wazwaz, Abdul Majid ^a  

^a SAINT XAVIER UNIVERSITY   (United States)

Author keywords

Cole Hopf transformation; DSSH equation; Hirota bilinear method; Multiple soliton solutions; Singular soliton solutions

Indexed keywords

NONLINEAR EQUATIONS;

COLE-HOPF TRANSFORMATION; DSSH EQUATION; HIROTA BILINEAR METHOD; MULTIPLE SOLITON SOLUTIONS; SINGULAR SOLITON SOLUTIONS;

SOLITONS;

EID: 58249091999     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.10.034     Document Type: Article

References (34)

1. Drinfeld V.G., and Sokolov V.V. Equations of Korteweg-de Vries type and simple Lie algebras. Dokl. Akad. Nauk. SSSR 258 (1981) 11-16
2. Satsuma J., and Hirota R. A coupled KdV equation is one of the four-reduction of the KP hierarchy. J. Phys. Soc. Jpn. 51 (1982) 3390-3397
3. Karsau-Kalkani A., and Yu Sarkovich S. Bäcklund transformation and special solutions for Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations. J. Phys. A: Math. Gen. 34 (2001) 7353-7358
4. Karsau-Kalkani A., Karsau A., Sakovich A., Sarkovich S., and Turhan R. A new integrable generalization of the Korteweg-de Vries equation. J. Math. Phys. 49 7 (2008) 1-10
5. Wazwaz A.M. Exact and explicit travelling wave solutions for the nonlinear Drinfeld-Sokolov system. Commun. Nonlinear Sci. Numer. Simul. 11 (2006) 311-325
6. Verhoeven C. Resonant triads for two bidirectional equations in the 1 + 1 dimensions. J. Phys. A: Math. Gen. 37 (2004) 10625-10638
7. Hirota R., and Ito M. Resonance of solitons in one dimension. J. Phys. Soc. Jpn. 52 3 (1983) 744-748
8. 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
9. Hirota R., and Satsuma J. N-soliton solutions of model equations for shallow water waves. J. Phys. Soc. Jpn. 40 2 (1976) 611-612
10. Hirota R. A new form of Bäcklund transformations and its relation to the inverse scattering problem. Prog. Theoret. Phys. 52 5 (1974) 1498-1512
11. Hirota R. The Direct Method in Soliton Theory (2004), Cambridge University Press, Cambridge
12. Hirota R. Exact solutions of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 18 (1971) 1192-1194
13. 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
14. 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
15. Hereman W., and Zhuang W. A MACSYMA program for the Hirota method. 13th World Congress on Computation and Applied Mathematics 2 (1991) 842-863
16. Hereman W., and Zhuang W. Symbolic computation of solitons with Macsyma. Comput. Appl. Math. II: Differen. Equat. (1992) 287-296
17. 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, 22-26.
18. 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
19. Wazwaz A.M. Multiple-front solutions for the Burgers equation and the coupled Burgers equations. Appl. Math. Comput. 190 (2007) 1198-1206
20. Wazwaz A.M. New solitons and kink solutions for the Gardner equation. Commun. Nonlinear Sci. Numer. Simul. 12 8 (2007) 1395-1404
21. Wazwaz A.M. Multiple-soliton solutions for the Boussinesq equation. Appl. Math. Comput. 192 (2007) 479-486
22. 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 1 (2008) 133-138
23. Wazwaz A.M. Multiple-front solutions for the Burgers-Kadomtsev-Petvisahvili equation. Appl. Math. Comput. 200 (2008) 437-443
24. Wazwaz A.M. Multiple-soliton solutions for the Lax-Kadomtsev-Petvisahvili (Lax-KP) equation. Appl. Math. Comput. 201 1/2 (2008) 168-174
25. 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
26. Wazwaz A.M. Multiple-soliton solutions of two extended model equations for shallow water waves. Appl. Math. Comput. 201 1/2 (2008) 790-799
27. Wazwaz A.M. Single and multiple-soliton solutions for the (2 + 1)-dimensional KdV equation. Appl. Math. Comput. 204 1 (2008) 20-26
28. Wazwaz A.M. Solitons and singular solitons for the Gardner-KP equation. Appl. Math. Comput. 204 1 (2008) 162-169
29. Wazwaz A.M. Regular soliton solutions and singular soliton solutions for the modified Kadomtsev-Petviashvili equations. Appl. Math. Comput. 204 1 (2008) 227-232
30. Wazwaz A.M. Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota's method, tanh-coth method and Exp-function method. Appl. Math. Comput. 202 (2008) 275-286
31. Malfliet W. The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Math. 164-165 (2004) 529-541
32. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 7 (1992) 650-654
33. Malfliet W., and Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys. Scripta 54 (1996) 563-568
34. Malfliet W., and Hereman W. The Tanh Method: II. Perturbation technique for conservative systems. Phys. Scripta 54 (1996) 569-575