New 5th-order Schwarzian evolution equations and their higher-order symmetries

Abstract

We report new quasilinear and fully-nonlinear 5th-order Schwarzian evolution equations. These are symmetry-integrable evolution equations in 1+1 dimensions, i.e. equations that admit Lie-B\"acklund symmetries, whereby it is required that the equations are kept invariant under the M\"obius transformation for their dependent variable.