Abstract
We give the exposition of a generalized symmetry approach toreduction of initial value problems for nonlinear evolutionequations in one spatial variable. Using this approach we classifythe initial value problems for third-order evolution equationsthat admit reduction to Cauchy problems for systems of twoordinary differential equations. These reductions are shown tocorrespond to higher conditional symmetries admitted by thecorresponding nonlinear evolution equations.
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Zhdanov, R.Z. Higher Conditional Symmetry and Reduction of Initial Value Problems. Nonlinear Dynamics 28, 17–27 (2002). https://doi.org/10.1023/A:1014962601569
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DOI: https://doi.org/10.1023/A:1014962601569