Abstract
Abstract The classification of scalar quasilinear integrable evolution equations of third order is completed, under the symmetry approach. A nonstandard way to represent an evolution equation in the form of a system is used, in order to simplify the calculations. The integrable nonlinearizable quasilinear equations are found to be related to the classical KdV and KN equations through differential substitutions. We formulate the conjecture that all the third order integrable evolution equations are related to these two equations or to the linear one through Miura-type differential substitutions.
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