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Multi-order exact solutions to the Drinfeld-Sokolov-Wilson equations. (English) Zbl 1233.83002

Summary: In this letter, based on the Lamé function and Jacobi elliptic function, the perturbation method is applied to the classical Drinfel’d-Sokolov-Wilson (hereafter DSW for short) equations, and many multi-order solutions are derived. It is shown that different Lamé functions can exist in the first order solutions of DSW system.

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
33E05 Elliptic functions and integrals
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[1] Wang, M. L., Phys. Lett. A, 199, 169 (1995)
[2] Fan, E. G., Phys. Lett. A, 277, 212 (2000)
[3] Wazwaz, A. M., Physica D, 213, 147 (2006)
[4] Hirota, R., J. Math. Phys., 14, 810 (1973)
[5] Otwinowski, M.; Paul, R.; Laidlaw, W. G., Phys. Lett. A, 128, 483 (1988)
[6] Kudryashov, N. A., Phys. Lett. A, 147, 287 (1990)
[7] Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Appl. Math. Mech., 22, 326 (2001)
[8] Yan, C. T., Phys. Lett. A, 224, 77 (1996)
[9] Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q., Phys. Lett. A, 289, 69 (2001)
[10] Fu, Z. T.; Liu, S. K.; Liu, S. D.; Zhao, Q., Phys. Lett. A, 290, 72 (2001)
[11] Dou, F. Q., Commun. Theor. Phys., 45, 1063 (2006)
[12] Sirendaoreji; Sun, J., Phys. Lett. A, 309, 387 (2003)
[13] Wu, G. J.; Han, J. H.; Zhang, W. L.; Zhang, M., Physica D, 229, 116 (2007)
[14] Liu, X. P.; Liu, C. P., Chaos Solitons Fractals, 39, 1915 (2009)
[15] He, J. H.; Wu, X. H., Chaos Solitons Fractals, 30, 700 (2006)
[16] Porubov, A. V., Phys. Lett. A, 221, 391 (1996)
[17] Porubov, A. V.; Velarde, M. G., J. Math. Phys., 40, 884 (1999)
[18] Porubov, A. V.; Parker, D. F., Wave Motion, 29, 97 (1999)
[19] Wang, Z. X.; Guo, D. R., Special Functions (1989), World Scientific: World Scientific Singapore · Zbl 0724.33001
[20] Liu, S. K.; Liu, S. D., Nonlinear Equations in Physics (2000), Peking University Press: Peking University Press Beijing
[21] Liu, G. T., Appl. Math. Comput., 212, 312 (2009)
[22] Nayfeh, A. H., Perturbation Methods (1973), John Wiley and Sons: John Wiley and Sons New York · Zbl 0375.35005
[23] Hirota, R.; Grammaticos, B.; Ramani, A., J. Math. Phys., 27, 1499 (1986)
[24] Liu, S. D.; Fu, Z. T.; Liu, S. K., Commun. Theor. Phys., 48, 425 (2007)
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