Similarity and conditional similarity reductions of a (2+1)-dimensional KdV equation via a direct method
作者： Sen-yue Lou , Xiao-yan Tang , Ji Lin
DOI: 10.1063/1.1320859
关键词:
摘要: To get the similarity solutions of a nonlinear physical equation, one may use the classical Lie group approach, nonclassical Lie group approach and the Clarkson and Kruskal (CK) direct …
scitation.org
harvard.edu
aip.org
sci-hub.se 
researchgate.net 参考文章(12)
Mark J. Ablowitz, David J. Kaup, Alan C. Newell, Harvey Segur, The Inverse scattering transform fourier analysis for nonlinear problems Studies in Applied Mathematics. ,vol. 53, pp. 249- 315 ,(1974) , 10.1002/SAPM1974534249
R. Radha, M. Lakshmanan, Dromion like structures in the (2+1)-dimensional breaking soliton equation Physics Letters A. ,vol. 197, pp. 7- 12 ,(1995) , 10.1016/0375-9601(94)00926-G
Peter A. Clarkson, Martin D. Kruskal, New similarity reductions of the Boussinesq equation Journal of Mathematical Physics. ,vol. 30, pp. 2201- 2213 ,(1989) , 10.1063/1.528613
Peter A. Clarkson, Simon Hood, New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations Journal of Mathematical Physics. ,vol. 35, pp. 255- 283 ,(1994) , 10.1063/1.530771
Sen‐yue Lou, Nonclassical symmetry reductions for the dispersive wave equations in shallow water Journal of Mathematical Physics. ,vol. 33, pp. 4300- 4305 ,(1992) , 10.1063/1.529988
Aurea Espinosa, Jorge Fujioka, Hydrodynamic Foundation and Painlevé Analysis of Hirota-Satsuma-Type Equations Journal of the Physical Society of Japan. ,vol. 63, pp. 1289- 1294 ,(1994) , 10.1143/JPSJ.63.1289
Elizabeth L. Mansfield, Peter A. Clarkson, Symmetries and exact solutions for a 2 + 1-dimensional shallow water wave equation Mathematics and Computers in Simulation. ,vol. 43, pp. 39- 55 ,(1997) , 10.1016/S0378-4754(96)00054-7
Petter A. Clarkson, Elizabeth L. Mansfield, Symmetry reductions and exact solutions of shallow water wave equations Acta Applicandae Mathematicae. ,vol. 39, pp. 245- 276 ,(1995) , 10.1007/978-94-011-0017-5_13
Ryogo Hirota, Junkichi Satsuma, N-Soliton Solutions of Model Equations for Shallow Water Waves Journal of the Physical Society of Japan. ,vol. 40, pp. 611- 612 ,(1976) , 10.1143/JPSJ.40.611
John Weiss, M. Tabor, George Carnevale, The Painlevé property for partial differential equations Journal of Mathematical Physics. ,vol. 24, pp. 522- 526 ,(1983) , 10.1063/1.525721