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On explicit exact solutions to the compound Burgers-KdV equation. (English) Zbl 0984.35138
Summary: Applying the theory of commutative algebra, we propose a new approach which is currently called the first integral method to study the compound Burgers-KdV equation and Burgers-KdV equation. The results indicate that the solutions obtained in the previous literature contain errors.

35Q53KdV-like (Korteweg-de Vries) equations
37K20Relations of infinite-dimensional systems with algebraic geometry, etc.
Full Text: DOI
[1] Wang, M.: Phys. lett. A. 213, 279 (1996)
[2] Johnson, R. S.: J. fluid mech.. 42, 49 (1970)
[3] Van Wijngaarden, L.: Ann. rev. Fluid mech.. 4, 369 (1972)
[4] Gao, G.: Sci. sinica ser. A. 28, 616 (1985)
[5] Grua, H.; Hu, P. W.: Phys. fluids. 10, 2596 (1967)
[6] Jeffrey, A.: Arch. mech.. 31, 559 (1979)
[7] Canosa, J.; Gazdag, J.: J. comp. Phys.. 23, 393 (1977)
[8] Dauletiyarov, K. Z.: Zh. vychisl. Mat. mat. Fiz.. 24, 383 (1984)
[9] Turetaev, I. D.: Comput. math. Math. phys.. 31, 69 (1991)
[10] Bona, J. L.; Schonbeck, M. E.: Proc. R. Soc. Edinburgh. 101A, 207 (1985)
[11] Guan, K. Y.; Gao, G.: Sci. sinica ser. A. 30, 64 (1987)
[12] Shu, J. J.: J. phys. A: math. Gen.. 20, L49 (1987)
[13] Gibbon, J. D.; Radmore, P.; Tabor, M.; Wood, D.: Stud. appl. Math.. 72, 39 (1985)
[14] Xiong, S. L.: Chin. sci. Bull.. 34, 1158 (1989)
[15] Liu, S. D.; Liu, S. K.; Ye, Q. X.: Math. pract. Theory. 28, 289 (1998)
[16] Jeffrey, A.; Xu, S.: Wave motion. 11, 559 (1989) · Zbl 0711.35125
[17] Jeffrey, A.; Mohamad, M. N. B.: Wave motion. 14, 369 (1991) · Zbl 0732.76012
[18] Halford, W. D.; Vlieg-Hulstman, M.: Wave motion. 14, 267 (1991)
[19] Parkes, E. J.; Duffy, B. R.: Phys. lett. A. 229, 217 (1997) · Zbl 1043.35521
[20] Pan, X. D.: Appl. math. Mech.. 9, 281 (1988)
[21] Ding, T. R.; Li, C. Z.: Ordinary differential equations. (1996)
[22] Bourbaki, N.: Commutative algebra. (1972) · Zbl 0279.13001
[23] Zhang, W. G.: Acta math. Sci.. 16, 241 (1996)