Bulg. J. Phys. vol.33 no.s2 (2006), pp. 211-222
Normalized Classes of Nonlinear Schrödinger Equations
R. Popovych
Institute of Mathematics of NAS of Ukraine, Tereshchenkivska Str., 01601 Kyiv, Ukraine
go backInstitute of Mathematics of NAS of Ukraine, Tereshchenkivska Str., 01601 Kyiv, Ukraine
Abstract. The notions of admissible transformations and normalized classes of differential equations are discussed. A series of nested normalized classes of nonlinear (1+1)-dimensional Schrödinger equations are constructed that gives description of all admissible point transformations in these classes. As an example of solving group classification with usage of normalization of the class under consideration, we classify Lie symmetries of the (1+1)-dimensional Schrödinger equations with potentials and logarithmic modular nonlinearity.