Wi. Fushchych et Ag. Nikitin, HIGHER SYMMETRIES AND EXACT-SOLUTIONS OF LINEAR AND NONLINEAR SCHRODINGER-EQUATION, Journal of mathematical physics, 38(11), 1997, pp. 5944-5959
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.