Abstract
We present a complete description of 2-dimensional equations that arise as symmetry reductions of four 3- dimensional Lax-integrable equations: (1) the universal hierarchy equation uyy = uzuxy− uyuxz; (2) the 3D rdDym equation uty = uxuxy− uyuxx; (3) the equation uty = utuxy− uyutx, which we call modified Veronese web equation; (4) Pavlov's equation uyy = utx + uyuxx− uxuxy.
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