Construction of generalized thermodynamic potentials by the Lie algebra method

The Lie group and Lie algebra are found basing on the analysis of the linearized system of differential equations describing the Williams domains in the nematic liquid crystal. By means of the algebra found, the nonlinear differential equation is obtained which is at the same time the Euler equation for the generalized thermodynamic potential (GTP) describing dissipative structures, the Williams domains. The GTP is found which describes the low-frequency regime of the Williams domains. The scheme described can also be applied to constructing the GTP of the high-frequency electrohydrodynamic instability.