Projective Lie symmetry of the potential Burgers equation
= Projective Lie symmetry of the potential Burgers equation
The vector field
$$
V=4t^2\partial_t+4tx\partial_x-(x^2+2t)\partial_u
$$
generates the local transformations
$$
T=\frac{t}{1-4\epsilon t},
\quad
X=\frac{x}{1-4\epsilon t},
\quad
U=u-\frac{\epsilon x^2}{1-4\epsilon t}
+\frac12\log(1-4\epsilon t).
$$
Its second prolongation sends $u_t-u_{xx}-u_x^2$ to $-8t$ times that expression, so it is a <Lie point symmetry> of the <potential Burgers equation>.