LAUSR

Hamiltonian Structures for Integrable Nonabelian Difference Equations

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1 Published in 2022 at "Communications in Mathematical Physics"

DOI: 10.1007/s00220-022-04348-3

Abstract: In this paper we extensively study the notion of Hamiltonian structure for nonabelian differential-difference systems, exploring the link between the different algebraic (in terms of double Poisson algebras and vertex algebras) and geometric (in terms… read more here.

Keywords: hamiltonian structures; difference; poisson; integrable nonabelian ... See more keywords

A new lattice hierarchy: Hamiltonian structures, symplectic map and N-fold Darboux transformation

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0 Published in 2019 at "Applied Mathematical Modelling"

DOI: 10.1016/j.apm.2018.10.030

Abstract: Abstract A new lattice hierarchy is constructed from a discrete matrix spectral problem. By the Tu scheme technique, the associated Hamiltonian structures and infinitely many conservation laws of this hierarchy are derived. Then a symplectic… read more here.

Keywords: symplectic map; lattice hierarchy; new lattice; darboux transformation ... See more keywords

Hamiltonian structures of isomonodromic deformations on moduli spaces of parabolic connections

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0 Published in 2021 at "Journal of the Mathematical Society of Japan"

DOI: 10.2969/jmsj/83858385

Abstract: In this paper, we treat moduli spaces of parabolic connections. We take \'etale coverings of the moduli spaces, and we construct a Hamiltonian structure of an algebraic vector field determined by the isomonodromic deformation for… read more here.

Keywords: parabolic connections; moduli spaces; isomonodromic deformations; structures isomonodromic ... See more keywords

On New Hamiltonian Structures of Two Integrable Couplings

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1 Published in 2022 at "Symmetry"

DOI: 10.3390/sym14112259

Abstract: In this paper, we present new Hamiltonian operators for the integrable couplings of the Ablowitz–Kaup–Newell–Segur hierarchy and the Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Hamiltonian structures are investigated. The involutive property is proven… read more here.

Keywords: structures two; hamiltonian structures; integrable couplings; two integrable ... See more keywords

Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds

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1 Published in 2018 at "Turkish Journal of Mathematics"

DOI: 10.3906/mat-1708-33

Abstract: We solve the equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds via Cartan’s method of equivalence. The problem separates into two branches on total space, one of which ends up with the intransitive… read more here.

Keywords: equivalence; equivalence problem; problem compatible; compatible hamiltonian ... See more keywords