An algebraic approach for solving evolution problems in some nonlinear quantum models

A new general Lie-algebraic approach is proposed for solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras supd(2) as their dynamic symmetry algebras. The method makes use of an expansion of the evolution operators by power series in the supd(2) shift operators and a (recursive) reduction finding coefficient functions for solving auxiliary exactly solvable su(2) problems with quadratic Hamiltonians. Zapotitlán 1994