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New exact solutions for three nonlinear evolution equations. (English) Zbl 0995.35003
Summary: By using general solutions of coupled Riccati equations and the relations between them a direct algebra method is described to construct several kinds of closed-form travelling wave solutions for some nonlinear differential equations. By this method three important nonlinear partial differential equations are studied and, in addition to re-deriving all known solutions, several new solutions are explicitly obtained with the aid of symbolic computation.

MSC:
35A08Fundamental solutions of PDE
Software:
MACSYMA
WorldCat.org
Full Text: DOI
References:
[1] Hereman, W.; Takaoka, M.: J. phys. A. 23, 4805 (1990) · Zbl 0719.35085
[2] Malfliet, W.: Am. J. Phys.. 60, 650 (1992)
[3] Parkes, E. J.: J. phys. A. 27, 497 (1994)
[4] Li, Z. B.: Mathematics mechanization and applications. 389 (2000) · Zbl 0968.68201
[5] Fan, E. G.: Phys. lett. A. 277, 212 (2000)
[6] Feng, X.: Int. J. Theor. phys.. 39, 207 (2000)
[7] Feng, X.: Phys. lett. A. 213, 167 (1996)
[8] Hu, J.: Phys. lett. A. 287, 81 (2001)
[9] Fan, E. G.: Phys. lett. A. 282, 18 (2001)
[10] Wang, M. L.; Zhou, Y. B.; Li, Z. B.: Phys. lett. A. 199, 169 (1995)
[11] Yao, R. X.; Li, Z. B.: Lecture notes series on computing. 9, 201 (2001)
[12] Wu, W. T.: Mechanical theorem proving in geometries: basic principles. (1994) · Zbl 0831.03003
[13] Sachs, R. L.: Physica D. 30, 1 (1988)
[14] Hirota, R.; Grammaticos, B.; Ramani, A.: J. math. Phys.. 27, 1499 (1986)
[15] Wu, Y. T.: Phys. lett. A. 255, 259 (1999)