Scalar second order evolution equations possessing an irreducible sl₂-valued zero curvature representation

by M. Marvan

J. Phys. A: Math. Gen.35 (2002) 9431–9439

Preprints: GA 1/2002 and DIPS 4/2002 and nlin.SI/0203043

All scalar second order evolution equations possessing an sl₂-valued zero curvature representation that is not reducible to a proper subalgebra of sl₂ are found. Saying all I mean all. Needless to say, none of the zero-curvature representations admits a parameter. The `simplest' of the equations is u_t = u² u_xx + 4 x u_x - 4 u³ - 4 u.