Applications of the lie algebraic formulas of Baker, Campbell, Hausdorff, and Zassenhaus to the calculation of explicit solutions of partial differential equations

Abstract

We apply Lie algebraic methods of the type developed by Baker, Campbell, Hausdorff, and Zassenhaus to the initial value and eigenvalue problems for certain special classes of partial differential operators which have many important applications in the physical sciences. We obtain detailed information about these operators including explicit formulas for the solutions of the problems of interest. We have also produced a computer program to do most of the intermediate algebraic computations.