Non-classical symmetry reduction: example of the Boussinesq equation

作者: D Levi , P Winternitz

DOI: 10.1088/0305-4470/22/15/010

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摘要: A symmetry of an equation will leave the set of all solutions invariant. A'conditional symmetry'will leave only a subset of solutions, defined by some differential condition, invariant. The …

参考文章(12)
George W. Bluman, Julian D. Cole, Similarity methods for differential equations ,(1974)
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
P. Rosenau, J.L. Schwarzmeier, On similarity solutions of Boussinesq-type equations Physics Letters A. ,vol. 115, pp. 75- 77 ,(1986) , 10.1016/0375-9601(86)90026-5
M. Boiti, F. Pempinelli, Similarity solutions and Bäcklund transformations of the Boussinesq equation Il Nuovo Cimento B. ,vol. 56, pp. 148- 156 ,(1980) , 10.1007/BF02738364
Peter J. Olver, Philip Rosenau, Group-invariant solutions of differential equations Siam Journal on Applied Mathematics. ,vol. 47, pp. 263- 278 ,(1987) , 10.1137/0147018
Peter J. Olver, Philip Rosenau, The construction of special solutions to partial differential equations Physics Letters A. ,vol. 114, pp. 107- 112 ,(1986) , 10.1016/0375-9601(86)90534-7