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

Abstract 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. Dedicated to Prof. W.I. Fushchych on the occasion of his 60th birthday