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.

19 pages, latex, to appear in J. Nonlinear Math. Phys

References in corpus (4)

• Integrable Theory of the Perturbation Equations
• The Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy
• Coupled Integrable Systems Associated with a Polynomial Spectral Problem and their Virasoro Symmetry Algebras
• Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras

Cited by in corpus (1)

• The generalised q-Wronskian solutions of the q-deformed constrained modified KP hierarchy