Mathematical Sciences: Algebraic Methods in Continuum Mechanics

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8901600 Olver This project is a continuation and deepening of research into various algebraic and geometric aspects of the equations of continuum mechanics and mathematical physics. The principal areas of concentration are Hamiltonian methods, equations of nonlinear elasiticity, and Cartan equivalence problems. Particular applications include: Hamiltonian structures and conservation laws for quasilinear hyperbolic systems, including gas dynamics and nonlinear elastic models, 2. multi-Hamiltonian systems and quantization, 3. nonlinear dissipation and normal forms for ordinary differential equations, 4. conservation laws, symmetries, canonical forms and invariants for planar elastic materials, 5. equilvalence problems from the calculus of variations, 6. Lie algebras and equivalence of differential operators with applications to molecular dynamics, and 7. classical invariant theory. Although the project covers a wide range of material, the different subjects inter-connect and reinforce each other in many ways, and the resulting combination of algebra, differential geometry and physical applications has proved to be an extremely fertile area of research.