Abstract The direct method developed by Clarkson and Kruskal (1989 J. Math. Phys. 30 2201) for finding the symmetry reductions of a nonlinear system is extended to find the conditional similarity solutions. Using the method of the Jimbo－Miwa (JM) equation, we find that three well-known (2+1)-dimensional models－the asymmetric Nizhnik--Novikov--Veselov equation, the breaking soliton equation and the Kadomtsev-Petviashvili equation－can all be obtained as the conditional similarity reductions of the JM equation.
Received: 20 July 2000
Revised: 15 May 2001
Accepted manuscript online:
(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
Fund: Project supported by the National Natural Science Foundation for Outstanding Young Scientists of China (Grant No. 19925522), by the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No. 2000024832) and by the Natural Science Foundation of Zheijiang Province, China.
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