Abstract
The relation between scalar evolution equations which are the integrability condition of sl(2,R)-valued linear problems with parameter (‘kinematic’ integrability) and those which possess recursion operators (‘formal’ integrability) is studied: using that kinematically integrable equations describe one-parameter families of pseudo-spherical surfaces and vice versa, it is shown that every second order formally integrable evolution equation is kinematically integrable, and that this result cannot be extended as proven to the third-order case.
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