Objective
The basic objectives of the project include:
analysis of fundamental geometric and algebraic structures arising in
equations of mechanics and mathematical physics;
application of modern cohomological methods to equations of mechanics and
mathematical physics, including construction Poisson (Hamiltonian)
structures, rrsion operators, series of symmetries and conservation laws;
generalization of the classical symmetry approach to nonlocal (including
integro-differential) and superdifferential equations;
development of algebraic and cohomological methods in the field theory and
their applications to BRST cohomologies and gauge invariant equations;
computations for particular equations of mechanics and mathematical physics;
development of computational methods for quantum symmetries
development of computer algebra systems to support these computations. The expected results of the Project are:
theoretical foundations of symmetry and cohomology approach to equations of
mechanics and mathematical physics;
analysis of specific problems of mechanics and mathematical physics,
including construction of determining equations for symmetries, conservation
laws, rrsion operators and Poisson structures, qualitative analysis of
these equations and creation of adequate nonlocal settings;
generalizations of symmetry and cohomology approach onto
integro-differential equations and construction of the corresponding
determining equations for basic invariants (see above);
analysis of cohomology invariants for gauge-invariant equations in relation
to field theory;
symbolic computations of symmetries, conservation laws, rrsion operators
and Poisson structures for specific equations of mechanics and mathematical
physics;
computer algebra systems for symbolic computations in the fields of
research. Dissemination of results:
preliminary and final reports will be accessible via Internet facilities in
the form of preprints;
final results will be published as journal papers;
publication of monographs in the field of research is planned (a preliminary
agreement with the Kluwer Academic Publishers has been made for two such
monographs).
Topic(s)
Data not availableCall for proposal
Data not availableFunding Scheme
Data not availableCoordinator
198SJ Amsterdam
Netherlands