We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. % Examples include equations of associativity of two-dimensional topological % field theory (WDVV equations). and various equations of Monge-Amp`ere % 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 $$ phi_{eta gamma}A^{eta}wedge A^{gamma}=0, $$ for some non-degenerate symmetric $phi$.
Systems of conservation laws with third-order Hamiltonian structures
Vitolo, Raffaele
2018-01-01
Abstract
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. % Examples include equations of associativity of two-dimensional topological % field theory (WDVV equations). and various equations of Monge-Amp`ere % 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 $$ phi_{eta gamma}A^{eta}wedge A^{gamma}=0, $$ for some non-degenerate symmetric $phi$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
