Objetivo
The ultimate goal of the project is the design of algorithmic criteria for the global integrability of physical field theories, which may later serve as the basis of new modelling and analysis technologies for industry. While the local integrability theory of partial differential equations is reasonably well understood and advanced mathematical techniques for its investigation exist, the study of global integrability has remained a challenging and highly risky task in mathematical physics for over a century. The proposed methodology combines hitherto unrelated results from various domains including algebraic topology, computer algebra, differential Galois theory, integrable systems and the formal theory of differential equations.
This approach originates in and relies on the complementary experiences of the partners in a research consortium newly formed specifically for this project. Recent advances in the mentioned domains and the inter-disciplinarity of the consortium let a real breakthrough in this old problem appear possible. Given the great importance of differential equations for the mathematical modelling in almost all sciences, such a breakthrough would lead to completely new possibilities in a wide range of fields spanning from fundamental physics over real-world engineering problems to social and economic sciences.
This includes the potential discovery of novel classes of topologically non-trivial solutions describing new physical phenomena, new approaches in non-linear stability and bifurcation theory or more powerful numerical methods rendering currently inaccessible problems tractable. The strong emphasis on algorithmic solutions will allow the later development of automatised toolboxes making sophisticated mathematical techniques avail able to industry.
Ámbito científico
- natural sciencesmathematicsapplied mathematicsmathematical physics
- natural sciencesmathematicspure mathematicstopologyalgebraic topology
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
- natural sciencesmathematicsapplied mathematicsnumerical analysis
- natural sciencesmathematicsapplied mathematicsmathematical model
Palabras clave
Convocatoria de propuestas
FP6-2003-NEST-A
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