1,278 research outputs found
Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling
Integrable couplings are associated with non-semisimple Lie algebras. In this
paper, we propose a new method to generate new integrable systems through
making perturbation in matrix spectral problems for integrable couplings, which
is called the `completion process of integrable couplings'. As an example, the
idea of construction is applied to the Ablowitz-Kaup-Newell-Segur integrable
coupling. Each equation in the resulting hierarchy has a bi-Hamiltonian
structure furnished by the component-trace identity
Construction and separability of nonlinear soliton integrable couplings
A very natural construction of integrable extensions of soliton systems is
presented. The extension is made on the level of evolution equations by a
modification of the algebra of dynamical fields. The paper is motivated by
recent works of Wen-Xiu Ma et al. (Comp. Math. Appl. 60 (2010) 2601, Appl.
Math. Comp. 217 (2011) 7238), where new class of soliton systems, being
nonlinear integrable couplings, was introduced. The general form of solutions
of the considered class of coupled systems is described. Moreover, the
decoupling procedure is derived, which is also applicable to several other
coupling systems from the literature.Comment: letter, 10 page
Dynamical tunneling in molecules: Quantum routes to energy flow
Dynamical tunneling, introduced in the molecular context, is more than two
decades old and refers to phenomena that are classically forbidden but allowed
by quantum mechanics. On the other hand the phenomenon of intramolecular
vibrational energy redistribution (IVR) has occupied a central place in the
field of chemical physics for a much longer period of time. Although the two
phenomena seem to be unrelated several studies indicate that dynamical
tunneling, in terms of its mechanism and timescales, can have important
implications for IVR. Examples include the observation of local mode doublets,
clustering of rotational energy levels, and extremely narrow vibrational
features in high resolution molecular spectra. Both the phenomena are strongly
influenced by the nature of the underlying classical phase space. This work
reviews the current state of understanding of dynamical tunneling from the
phase space perspective and the consequences for intramolecular vibrational
energy flow in polyatomic molecules.Comment: 37 pages and 23 figures (low resolution); Int. Rev. Phys. Chem.
(Review to appear in Oct. 2007
Bi-Integrable and Tri-Integrable Couplings of a Soliton Hierarchy Associated with S
Based on the three-dimensional real special orthogonal Lie algebra SO(3), by zero curvature equation, we present bi-integrable and tri-integrable couplings associated with SO(3) for a hierarchy from the enlarged matrix spectral problems and the enlarged zero curvature equations. Moreover, Hamiltonian structures of the obtained bi-integrable and tri-integrable couplings are constructed by applying the variational identities
Tachyon Backgrounds in 2D String Theory
We consider the construction of tachyonic backgrounds in two-dimensional
string theory, focusing on the Sine-Liouville background. This can be studied
in two different ways, one within the context of collective field theory and
the other via the formalism of Toda integrable systems. The two approaches are
seemingly different. The latter involves a deformation of the original inverted
oscillator potential while the former does not. We perform a comparison by
explicitly constructing the Fermi surface in each case, and demonstrate that
the two apparently different approaches are in fact equivalent.Comment: 25 pages, no figure
Yang-Baxter algebra and generation of quantum integrable models
An operator deformed quantum algebra is discovered exploiting the quantum
Yang-Baxter equation with trigonometric R-matrix. This novel Hopf algebra along
with its limit appear to be the most general Yang-Baxter algebra
underlying quantum integrable systems. Three different directions of
application of this algebra in integrable systems depending on different sets
of values of deforming operators are identified. Fixed values on the whole
lattice yield subalgebras linked to standard quantum integrable models, while
the associated Lax operators generate and classify them in an unified way.
Variable values construct a new series of quantum integrable inhomogeneous
models. Fixed but different values at different lattice sites can produce a
novel class of integrable hybrid models including integrable matter-radiation
models and quantum field models with defects, in particular, a new quantum
integrable sine-Gordon model with defect.Comment: 13 pages, revised and bit expanded with additional explanations,
accepted for publication in Theor. Math. Phy
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