Symmetry Reduction and Cauchy Problems for a Class of
Fourth-Order Evolution Equations |
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Authors: | LI Ji-Na and ZHANG Shun-Li |
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Institution: | 1. Center for Nonlinear Studies, Department of Mathematics,
Northwest University, Xi'an 710069, China
;2. Center of Nonlinear Science, Ningbo University, Ningbo 315211, China |
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Abstract: | We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations to Cauchy problems for systems of ordinary differential equations (ODEs). We classify a class of fourth-order evolution equations which admit certain
higher-order generalized conditional symmetries (GCSs) and give some examples to show the main reduction procedure. These reductions cannot be derived within the framework of the standard Lie approach, which hints that the technique presented here is
something essential for the dimensional reduction of evolution equations. |
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Keywords: | fourth-order evolution equation generalized conditional symmetry Cauchy problem |
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