  By starting from known graded Lie algebras, including Virasoro algebras, new
kinds of time-dependent evolution equations are found possessing graded
symmetry algebras. The modified KP equations are taken as an illustrative
example: new modified KP equations with $m$ arbitrary time-dependent
coefficients are obtained possessing symmetries involving $m$ arbitrary
functions of time. A particular graded symmetry algebra for the modified KP
equations is derived in this connection homomorphic to the Virasoro algebras.
