An Algebraic Approach to Solving Evolution Problems in Some Nonlinear   Quantum Models
  A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras.   The method makes use of an expansion of the evolution operators by power series in the $su_{pd}(2)$ shift operators and a (recursive) reduction of finding coefficient functions to solving auxiliary exactly solvable $su(2)$ problems with quadratic Hamiltonians.   PACS numbers: 03.70; 02.20; 42.50 
Valery P. Karassiov and Andrei B. Klimov (P.N. Lebedev Physical   Institute)