arXiv subjects

Stoimen Stoimenov

Publications and source records attributed to Stoimen Stoimenov.

21 records · Page 2Linked to original sources

arXiv2005

Lie symmetries of semi-linear Schrödinger equations and applications

Conditional Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra conf_3. The corresponding representations of the parabolic and almost-parabolic subalgebras of conf_3 are classified and the complete list of conditionally invariant semi-linear Schrödinger equations is obtained. Applications to the phase-ordering kinetics of simple magnets and to simple particle-reaction models are briefly discussed.

math-ph↗

arXiv2005

On the dynamical symmetric algebra of ageing: Lie structure, representations and Appell systems

The study of ageing phenomena leads to the investigation of a maximal parabolic subalgebra of conf_3 which we call alt. We investigate its Lie structure, prove some results concerning its representations and characterize the related Appell systems.

math.AP↗

arXiv2005

Dynamical symmetries of semi-linear Schrödinger and diffusion equations

Conditional and Lie symmetries of semi-linear 1D Schrödinger and diffusion equations are studied if the mass (or the diffusion constant) is considered as an additional variable. In this way, dynamical symmetries of semi-linear Schrödinger equations become related to the parabolic and almost-parabolic subalgebras of a three-dimensional conformal Lie algebra conf_3. We consider non-hermitian representations and also include a dimensionful coupling constant of the non-linearity. The corresponding representations of the parabolic and almost-parabolic subalgebras of conf_3 are classified and the complete list of conditionally invariant semi-linear Schrödinger equations is obtained. Possible applications to the dynamical scaling behaviour of phase-ordering kinetics are discussed.

math-ph↗