We establish a group-invariant version of the variational bicomplex that is based on a general moving frame construction. The main application is an explicit group-invariant formula for the Euler-Lagrange equations of an invariant variational problem.

We derive simple explicit formulas for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and give applications to the Fredholm modules and equivariant characteristic classes.

Manuscript received April 8, 1999. Manuscript revised September 8, 1999. † The author is with the Dept. of Lightwave Sciences, Osaka Electro-Communication University, Neyagawa-shi, 572-8530 Japan. a) E-mail: [email protected] SUMMARY The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua’s integ...

Multisymplecticity and the variational bicomplex are two subjects which have developed independently. Our main observation is that re-analysis of multisymplectic systems from the view of the variational bicomplex not only is natural but also generates new fundamental ideas about multisymplectic Hamiltonian PDEs. The variational bicomplex provides a natural grading of differential forms accordin...

Generalized matrix Lotka-Volterra lattice equations are obtained in a systematic way from a “master equation” possessing a bicomplex formulation.

We derive simple explicit formula for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and apply it to write formulas for the equivariant Chern character and characters of finitely-summable bounded Fredholm modules.

We show how the homogeneous variational bicomplex provides a useful formalism for describing a number of properties of single-integral variational problems, and we introduce a subsequence of one of the rows of the bicomplex which is locally exact with respect to the variational derivative. We are therefore able to recover a Lagrangian from a set of equations given as a variationally-closed diff...