Symmetries and integration of differential equations.
Symmetries and invariant differential pairings.
Symmetries in finite order variational sequences
We refer to Krupka’s variational sequence, i.e. the quotient of the de Rham sequence on a finite order jet space with respect to a ‘variationally trivial’ subsequence. Among the morphisms of the variational sequence there are the Euler-Lagrange operator and the Helmholtz operator. In this note we show that the Lie derivative operator passes to the quotient in the variational sequence. Then we define the variational Lie derivative as an operator on the sheaves of the variational sequence. Explicit...
Symmetries of connections on fibered manifolds
The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.
Symmetries of Conservation Laws
Symmetries of factor systems.
Symmetry and local conjugacy on complex manifolds.
Symmetry and Overdetermined Boundary Value Problems.
Symmetry group of Ţiţeica surfaces PDE.
Symmetry groups and conservation laws of certain partial differential equations.
Symmetry groups and Lagrangians associated with Tzitzeica surfaces.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry Lie group of the Monge-Ampère equation.
Symmetry of local minimizers for the three-dimensional Ginzburg–Landau functional
We classify nonconstant entire local minimizers of the standard Ginzburg–Landau functional for maps in satisfying a natural energy bound. Up to translations and rotations,such solutions of the Ginzburg–Landau system are given by an explicit solution equivariant under the action of the orthogonal group.
Symmetry of the barochronous motions of a gas.
Symmetry of the Ginzburg-Landau minimizer in a disc
Symmetry operators of a Hartree-type equation with quadratic potential.
Symmetry Properties of Singularities of C°°-Functions.
Symplectic classification of parametric complex plane curves
Based on the discovery that the δ-invariant is the symplectic codimension of a parametric plane curve singularity, we classify the simple and uni-modal singularities of parametric plane curves under symplectic equivalence. A new symplectic deformation theory of curve singularities is established, and the corresponding cyclic symplectic moduli spaces are reconstructed as canonical ambient spaces for the diffeomorphism moduli spaces which are no longer Hausdorff spaces.
Symplectic critical surfaces in Kähler surfaces
Let be a Kähler surface and be a closed symplectic surface which is smoothly immersed in . Let be the Kähler angle of in . We first deduce the Euler-Lagrange equation of the functional in the class of symplectic surfaces. It is , where is the mean curvature vector of in , is the complex structure compatible with the Kähler form in , which is an elliptic equation. We call such a surface a symplectic critical surface. We show that, if is a Kähler-Einstein surface with nonnegative...