Ansatzes and exact solutions for nonlinear Schrodinger equations
  We consider construction of ansatzes for nonlinear Schrodinger equations in three space dimensions and arbitrary nonlinearity, and conditions of their reduction to ordinary differential equations. Complete description of ansatzes of certain types is presented. We also discuss the relationship between solutions, and both Lie and conditional symmetry of these equations. 
Irina Yehorchenko
math-ph math.AP math.MP nlin.SI