Abstract
Lie point symmetries associated with the new (2+1)-dimensional KdV equation u t + 3u x u y + u xxy = 0 are investigated. Some similarity reductions are derived by solving the corresponding characteristic equations. Painlevé analysis for this equation is also presented and the soliton solution is obtained directly from the Bäcklund transformation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Olver P J. Applications of Lie Groups to Differential Equations, New York: Springer-Verlag, 1986.
Bluman G W, Kumei S. Symmetries and Differential Equations, New York: Springer-Verlag, 1989.
Weiss J, Tabor M, Carnevale G. The Painlevé property for partial differential equations, J Math Phys, 1983, 24: 522–526.
Jimbo M, Kruskal M D, Miwa T. Painlevé test for the self-dual Yang-Mills equations, Phys Lett A, 1982, 92: 59–60.
Conte R. Invariant Painlevé analysis for partial differential equations, Phys Lett A, 1989, 140: 383–390.
Lou S Y. Extended Painlevé expansion, non-standard truncation and special reductions of non-linear evolution equations, Z Naturforsch A, 1998, 53: 251–258.
Zhang Y F, Honwah T, Zhao J. Higher-dimensional KdV equations and their soliton solutions, Commun Theor Phys, 2006, 45: 411–413.
Shen S F. General multi-linear variable separation approach to solving low dimensional nonlinear systems and localized exitations, Acta Phys Sinica, 2006, 55: 1011–1015.
Shen S F, Zhang J, Pan Z L. Coherent structures of some (1+1)-dimensional nonlinear systems, Phys Lett A, 2005, 339: 52–62.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shen, S. Lie symmetry analysis and Painlevé analysis of the new (2+1)-dimensional KdV equation. Appl. Math. Chin. Univ. 22, 207–212 (2007). https://doi.org/10.1007/s11766-007-0209-2
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11766-007-0209-2