Abstract:
Based on key elements of Olver's approach to partial differential equations for Hamiltonian evolution, we propose an algebraic construction appropriate for Hamiltonian evolutionary systems with constraints.
Keywords:
differential algebra, differential bicomplex, Lie–Poisson structure, Hamiltonian map, Hamiltonian evolution system of partial differential equations, constraint.
Citation:
V. V. Zharinov, “Lie–Poisson structures over differential algebras”, TMF, 192:3 (2017), 459–472; Theoret. and Math. Phys., 192:3 (2017), 1337–1349
This publication is cited in the following 6 articles:
A. K. Gushchin, “Extensions of the space of continuous functions and embedding theorems”, Sb. Math., 211:11 (2020), 1551–1567
A. K. Gushchin, “The boundary values of solutions of an elliptic equation”, Sb. Math., 210:12 (2019), 1724–1752
A. K. Gushchin, “On the Existence of L2 Boundary Values of Solutions to an Elliptic Equation”, Proc. Steklov Inst. Math., 306 (2019), 47–65
V. V. Zharinov, “Hamiltonian operators with zero-divergence constraints”, Theoret. and Math. Phys., 200:1 (2019), 923–937
A. K. Gushchin, “A criterion for the existence of Lp boundary values of solutions to an elliptic equation”, Proc. Steklov Inst. Math., 301 (2018), 44–64
V. V. Zharinov, “Hamiltonian operators in differential algebras”, Theoret. and Math. Phys., 193:3 (2017), 1725–1736