TY - RPRT
T1 - On deformations of multidimensional Poisson brackets of hydrodynamic type
Y1 - 2013
A1 - Matteo Casati
KW - Hamiltonian operator
AB - The theory of Poisson Vertex Algebras (PVAs) is a good framework to treat Hamiltonian partial differential equations. A PVA consist of a pair $(\mathcal{A},\{\cdot_{\lambda}\cdot\})$ of a differential algebra $\mathcal{A}$ and a bilinear operation called the $\lambda$-bracket. We extend the definition to the class of algebras $\mathcal{A}$ endowed with $d\geq 1$ commuting derivations. We call this structure a multidimensional PVA: it is a suitable setting to the study of deformations of the Poisson bracket of hydrodynamic type associated to the Euler's equation of motion of $d$-dimensional incompressible fluids. We prove that for $d=2$ all the first order deformations of such class of Poisson brackets are trivial.
PB - SISSA
UR - http://hdl.handle.net/1963/7235
U1 - 7271
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -