Non-local symmetry of equation of one-dimensional flow of a sub- isothermal glacier (Q1333643)

Computing the symmetry group for the equation \[ {\partial \ell \over \partial t} = {\partial \over \partial x} \left\{ (\ell - \ell_0)^2f \Biggl[ (\ell - \ell_0) \Bigl |{ \partial \ell \over \partial x} \Bigr |\Biggr] \right\} \] yields a 6-parametric group \(t' = \alpha_1 + \alpha_4t\), \(x'=\alpha_2+\alpha_5x\), \(v' = \alpha_3 + \alpha_6v\), where \(\ell - \ell_0 = v_x\). Here \(\ell - \ell_0\) is the thickness of a glacier, \(\ell_0 (x)\) is the basement level, \(f\) is a function determined by the ice rheology.