A group analysis of a class of drift-diiusion systems is performed. In account of the presence of arbitrary constitutive functions, we look for Lie symmetries starting from the weak equivalence transformations. Applications to the transport of charges in semiconductors are presented and a special class of solutions is given for particular doping prooles.
By using the Lie's invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. Starting from the equivalence generators we construct the differential invariants of order one. We apply these latter ones to find the most general subclass of variable… (More)
The equivalence transformation algebra L E for the class of equations u t − u xx = f (u, u x) is obtained. After getting the differential invariants with respect to L E , some results which allow to linearize a subclass of equations are showed. Equations like the standard deter-ministic KPZ equation fall in this subclass.