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By starting from known graded Lie algebras, including Virasoro algebras, newkinds of time-dependent evolution equations are found possessing gradedsymmetry algebras. The modified KP equations are taken as an illustrativeexample: new modified KP equations with $m$ arbitrary time-dependentcoefficients are obtained possessing symmetries involving $m$ arbitraryfunctions of time. A particular graded symmetry algebra for the modified KPequations is derived in this connection homomorphic to the Virasoro algebras.Comment: 19 pages, latex, to appear in J. Nonlinear Math. Phy

Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP Equations