相关论文: Discretization, Moyal, and integrability

Domains of condensed-phase monolayers of chiral molecules exhibit a variety of interesting nonequilibrium structures when formed via pressurization. To model these domain patterns, we add a complex field describing the tilt degree of…

We consider the micellization of block copolymers in solution, employing self consistent field theory with an additional constraint that permits the examination of intermediate structures. From the information for an isolated micelle…

New extensions of the KP and modified KP hierarchies with self-consistent sources are proposed. The latter provide new generalizations of $(2+1)$-dimensional integrable equations, including the DS-III equation and the $N$-wave problem.…

We construct a symplectic integrator for non-separable Hamiltonian systems combining an extended phase space approach of Pihajoki and the symmetric projection method. The resulting method is semiexplicit in the sense that the main time…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

The multisymplectic structure of the KP equation is obtained directly from the variational principal. Using the covariant De Donder-Weyl Hamilton function theories, we reformulate the KP equation to the multisymplectic form which proposed…

We give the {\it spectral decomposition} of the path space of the $U_q(\hatsl)$ vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the $\hatsl$ level $l$ integrable modules,…

Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective…

A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and…

The paper gives sharp spectral gap conditions for existence of inertial manifolds for abstract semilinear parabolic equations with non-self-adjoint leading part. Main attention is paid to the case where this leading part have Jordan cells…

Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…

In this paper, we constructed the addition formulae for several integrable hierarchies, including the discrete KP, the q-deformed KP, the two-component BKP and the D type Drinfeld-Sokolov hierarchies. With the help of the Hirota bilinear…

In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a…

Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant…

A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional ``phase space'' variables $(k,x)$ of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions…

Integrable hierarchies associated with the singular sector of the KP hierarchy, or equivalently, with $\dbar$-operators of non-zero index are studied. They arise as the restriction of the standard KP hierarchy to submanifols of finite…

A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.

We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional and the connectedness constraint of (Dondl, Lemenant,…

In presence of dissipation, quantal states may acquire complex-valued phase effects. We suggest a notion of dissipative interferometry that accommodates this complex-valued structure and that may serve as a tool for analyzing the effect of…

Phase Space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective hamiltonian invariants. The power and simplicity of the method is fully illustrated through new…