Fu, Zuntao; Yuan, Naiming; Chen, Zhe; Mao, Jiangyu; Liu, Shikuo Multi-order exact solutions to the Drinfeld-Sokolov-Wilson equations. (English) Zbl 1233.83002 Phys. Lett., A 373, No. 41, 3710-3714 (2009). 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. Cited in 2 Documents MSC: 83C15 Exact solutions to problems in general relativity and gravitational theory 33E05 Elliptic functions and integrals Keywords:DSW equations; perturbation method; Lamé function; Jacobi elliptic function; multi-order solutions PDFBibTeX XMLCite \textit{Z. Fu} et al., Phys. Lett., A 373, No. 41, 3710--3714 (2009; Zbl 1233.83002) Full Text: DOI References: [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) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.