Related papers: New Hamiltonian formalism and Lagrangian represent…
In the present work, we study Hamiltonian systems on (co)adjoint orbits and propose a Lax pair formalism for Gelfand-Tsetlin integrable systems defined on (co)adjoint orbits of the compact Lie groups ${\rm{U}}(n)$ and ${\rm{SO}}(n)$. In the…
A realization of various algebraic structures in terms of the $C_{\lambda}$-extended oscillator algebras is introduced. In particular, the $C_{\lambda}$-extended oscillator algebras realization of Fairlie-Fletcher-Zachos (FFZ)algebra is…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar…
A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by…
This paper gives a new way of constructing Landau-Ginzburg mirrors using deformation theory of Lagrangian immersions motivated by the works of Seidel, Strominger-Yau-Zaslow and Fukaya-Oh-Ohta-Ono. Moreover we construct a canonical functor…
We introduce the notions of generalised (bi-)Hamiltonian structures which generalise naturally the (bi-)Hamiltonian structures of evolutionary partial differential equations. In the hydrodynamic case, these structures are characterised in…
The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether's conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this…
We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…
This work provides an introduction and overview on some basic mathematical aspects of the single-flux Aharonov-Bohm Schr\"odinger operator. The whole family of admissible self-adjoint realizations is characterized by means of four different…
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…
In the framework of polysymplectic Hamiltonian formalism, degenerate Lagrangian field systems are described as multi-Hamiltonian systems with Lagrangian constraints. The physically relevant case of degenerate quadratic Lagrangians is…
The barotropic ideal fluid with step and delta-function discontinuities coupled to Einstein's gravity is studied. The discontinuities represent star surfaces and thin shells; only non-intersecting discontinuity hypersurfaces are considered.…
We consider hydrodynamic chains in $(1+1)$ dimensions which are Hamiltonian with respect to the Kupershmidt-Manin Poisson bracket. These systems can be derived from single $(2+1)$ equations, here called hydrodynamic Vlasov equations, under…
An alternative version of Hamiltonian formalism for higher-derivative theories is presented. It is related to the standard Ostrogradski approach by a canonical transformation. The advantage of the approach presented is that the Lagrangian…
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the…
We propose a physical interpretation of the chiral de Rham complex as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model. We show that the chiral de Rham complex on a Calabi-Yau manifold carries all information…
By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are…
We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a…
In this paper we derive a new formulation of the water waves equations with vorticity that generalizes the well-known Zalkarov-Craig-Sulem formulation used in the irrotational case. We prove the local well-posedness of this formulation, and…