HIGHER SYMMETRIES AND EXACT-SOLUTIONS OF LINEAR AND NONLINEAR SCHRODINGER-EQUATION

A new approach for the analysis of partial differential equations is d eveloped which is characterized by a simultaneous use of higher and co nditional symmetries. Higher symmetries of the Schrodinger equation wi th an arbitrary potential are investigated. Nonlinear determining equa tions for potentials are solved using reductions to Weierstrass, Painl eve, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetr ies are used to generate families of exact solutions of linear and non linear Schrodinger equations. (C) 1997 American Institute of Physics.