Systems of conservation laws with third-order Hamiltonian structures

Abstract

We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences of lines in ${\mathbb{P}}^{n+2}$ satisfying additional geometric constraints. Algebraically, the problem can be reformulated as follows: for a vector space $W$ of dimension $n+2$, classify $n$-tuples of skew-symmetric 2-forms $A^{\alpha }\in {\Lambda }^2(W)$ such that \[ ϕ_{βγ}A^β\wedge A^γ=0, \] for some non-degenerate symmetric $\varphi$.

31 pages

References in corpus (2)

• On the Mathematical and Geometrical Structure of the Determining Equations for Shear Waves in Nonlinear Isotropic Incompressible Elastodynamics
• Linear Congruences and hyperbolic Systems of conservation Laws

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