Two new classes of exact solutions for the KdV equation via Bäcklund transformations

Chaos, Solitons and Fractals

Volumn 8, Issue 12, 1997, Pages 1901-1909

  Khater, A H ^a,c   El Kalaawy, O H ^a   Helal, M A ^b  

^a Beni Suef University   (Egypt)

^b CAIRO UNIVERSITY   (Egypt)

^c UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS;

BACKLUND TRANSFORMATIONS (BC); KORTEWEG DE VRIES (KDV) EQUATIONS;

ELECTROMAGNETIC WAVE PROPAGATION;

EID: 0031342907     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(97)00090-8     Document Type: Article

References (34)

1. Dodd, R. K., Eilbeck, J. C., Gibbon, J. D. and Morris, H. C., Solitons and Nonlinear Waves Equation. Academic Press, New York, 1982.
2. Whitham, G. B., Linear and Nonlinear Waves. Wiley, New York, 1974.
3. Lamb, G. L., Elements of Soliton Theory. Wiley, New York, 1980.
4. Ablowitz, M. J. and Clarkson, P. A., Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge, 1991.
5. Rogers, C. and Shadwick, W. E., Bäcklund Transformations and their Applications. Academic Press, New York, 1982.
6. Wiess, J., Tabor, M. and Garnevale, G., J. Math. Phys., 1983, 24, 522.
7. Khater, A. H., Astrophys. Space Sci., 1989, 162, 151.
8. Khater, A. H., El-Sabbagh, M. F. and Callebaut, D. K., Annal. Soc. Sci. de Bruxelles, 1987, T101III, 99.
9. Khater, A. H., El-attary, M. A., El-Sabbagh, M. F. and Callebaut, D. K., Astrophys. Space Sci., 1988, 149, 217.
10. Khater, A. H., El-Sabbagh, M. F. and Callebaut, D. K., Comput. Math. Applic., 1988, 17, 1379.
11. Olver, P. J., Applications of Lie Groups to Differential Equations. Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, Berlin, 1986.
12. Hereman, W., Korpel, A. and Banerjee, P. P., Wave Motion, 1985, 7, 283.
13. Hereman, W., Banerjee, P.P., Korpel, A., Assanto, G., Van Immerzeel, A. and Mee-poel, A., J. Phys. A, 1986, 19, 607.
14. Hereman, W., In Proceedings of Conference on Applied Mathematics, Cairo, Egypt, 1987, p. 291.
15. Hereman, W., Banerjee, P. P. and Chatterjee, M. R., J. Phys. A, 1989, 22, 241.
16. Hereman, W. and Takaoka, M., J. Phys. A. 1990, 23, 4805.
17. Malfliet, W., J. Phys. A, 1980, 13, 2929.
18. Malfliet, W., J. Phys. A, 1991, 24, 5499.
19. Malfliet, W., Am. J. Phys., 1992, 60, 650.
20. Malfliet, W., J. Phys. A, 1993, 26, L.723.
21. Wahlquist, H. D. and Estabrook, F. B., Phys. Rev. Lett., 1973, 31, 1386.
22. Zakharov, V. E. and Shabat, A. B., Soviet Phys. JETP, 1972, 34, 1403.
23. Wadati, M., J. Phys. Soc. Jpn., 1974, 36, 1498.
24. Lamb, G. L., J. Math. Phys., 1974, 15, 2157.
25. Levi, O., Rognisco, D. and Sym, A., Lett. Nuovo Cim., 1982, 33, 401.
26. Porsezian, K., J. Phys. A, 1991, 24, 337.
27. Chan, W. L. and Zheng, Y. K., J. Austral. Math. Soc. Ser. B, 1989, 30, 313.
28. Wadati, M., Sunuki, H. and Konno, K., Progr. Theor. Phys., 1975, 53, 419.
29. Konno, K. and Wadati, M., Progr. Theoret. Phys., 1975, 53, 1652.
30. Khater, A. H., Shamardan, A. B., Callebaut, D. K. and Ibrahim, R. S., IMA J. Appl. Math., 1997, 58, 51.
31. Khater, A. H. and Ibrahim, R. S., submitted to J. Math. Anal. & Applic.
32. Eisenhart, L., A Treatise on the Differential Geometry of Curves and Surfaces. Dover, New York, 1960.
33. Forsyth, A. R., Theory of Differential Equations, Vol. 6. Dover, New York, 1959.
34. Airy, G. B., Tides and waves. In Encyclopedia Metropolotana, Vol. 5. London, 1845, p. 241.