The Ginzburg–Landau equations were proposed in the superconductivity theory to describe mathematically intermediate state of superconductors which normal conductivity is mixed with superconductivity. It turned out that these have interesting and non-trivial generalizations. First all, they can be extended arbitrary compact Riemann surfaces. Next, generalized dimension 3 as dynamical (or hyperbo...

Let D = Ω\ω ⊂ R be a smooth annular type domain. We consider the simplified Ginzburg-Landau energy Eε(u) = 12 ∫

Ginzburg-Landau functional is derived for a system possessing both chiral and diquark condensates. Anderson theorem for such a system is formulated and proved.

Ginzburg-Landau functional is derived for a system possessing both chiral and diquark condensates. Anderson theorem for such a system is formulated and proved.

Group classification of the generalized complex Ginzburg-Landau equations is presented. An approach to group classification of systems of reaction-diffusion equations with general diffusion matrix is formulated.

We compute the smooth cohomology (both unrestricted and compactly supported) of the supercharge of an ultraviolet cutoo N = 2 supersymmetric Landau-Ginzburg eld theory.

We investigate the stability of the square vortex lattice which has been recently observed in experiments on the borocarbide family of superconductors. Taking into account the tetragonal symmetry of these systems, we add fourfold symmetric fourth-derivative terms to the Ginzburg-Landau(GL) free energy. At Hc2 these terms may be treated perturbatively to lowest order to locate the transition fro...

The study of the integrability properties of the N=2 Landau-Ginzburg models leads naturally to a graph generalization of the Yang-Baxter equation which synthetizes the well known vertex and RSOS Yang-Baxter equations.A non trivial solution of this equation is found for the t2 perturbation of the A-models, which turns out to be intimately related to the Boltzmann weights of a Chiral-Potts model....

Essential to the derivation of the Ginzburg-Landau equation is assumption that the spatial variables of the vector field U(x, y, t) are defined on a cylindrical domain. This means that (x, y) ∈ R ×Ω, where Ω ⊂ R is a open and bounded domain (and m ≥ 1, n ≥ 0), so that U : R ×Ω×R+ → R . The N ×N constant coefficient matrix Sμ is assumed to be non-negative, in the sense that all its eigenvalues a...

Group classification of the generalized complex Ginzburg-Landau equations is presented. An approach to group classification of systems of reaction-diffusion equations with general diffusion matrix is developed.