Proceeding di conferenze
|Lie symmetries of semi-linear Schroedinger equations and applications|
|Stoimenov S., Henkel M.|
|Journal of Physics: Conference Series 40 (2006) 144|
|DOI : 10.1088/1742-6596/40/1/018|
|ArXiv : math-ph/0512025 [PDF]|
Conditional Lie symmetries of semi-linear 1D Schroedinger and diffusion equations are studied in case the mass (or the diffusion constant) is considered as an additional variable and/or where the couplings of the non-linear part have a non-vanishing scaling dimension. In this way, dynamical symmetries of semi-linear Schroedinger equations become related to certain subalgebras of a three-dimensional conformal Lie algebra (conf3) C. The representations of these subalgebras are classified and the complete list of conditionally invariant semi-linear Schroedinger equations is obtained. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.