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Cauchy Problems for KdV-type Equations and Higher-Order Conditional Symmetries |
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| Authors: | LI Ji-Na ZHANG Shun-Li ZUO Su-Li |
| Affiliation: | 1. Center for Nonlinear Studies, Department of Mathematics, Northwest University,Xi'an 710069, China;2. Center of Nonlinear Science, Ningbo University, Ningbo 315211, China |
| Abstract: | We develop the generalized conditional symmetry (GCS) approach to solve the problem of dimensional reduction of Cauchy problems for the KdV-type equations. We characterize these equations that admit certain higher-order GCSs and show the main reduction procedure by some examples. The obtained reductions cannot be derived within the framework of the standard Lie approach. |
| Keywords: | KdV-type equations generalized conditional symmetry Cauchy problem |
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