5,966 research outputs found
Darboux transformation with dihedral reduction group
We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix, we obtain local conservation laws of the system
Reductions of integrable equations on A.III-type symmetric spaces
We study a class of integrable non-linear differential equations related to
the A.III-type symmetric spaces. These spaces are realized as factor groups of
the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to
this symmetric space as an element of the reduction group and restrict generic
Lax operators to this symmetric space. The symmetries of the Lax operator are
inherited by the fundamental analytic solutions and give a characterization of
the corresponding Riemann-Hilbert data.Comment: 14 pages, 1 figure, LaTeX iopart styl
Formal diagonalisation of Lax-Darboux schemes
We discuss the concept of Lax-Darboux scheme and illustrate it on well known
examples associated with the Nonlinear Schrodinger (NLS) equation. We explore
the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model,
principal chiral field model as well as with differential-difference integrable
systems (including the Toda lattice and differential-difference Heisenberg
chain) and integrable partial difference systems. We show that there exists a
transformation which formally diagonalises all elements of the Lax-Darboux
scheme simultaneously. It provides us with generating functions of local
conservation laws for all integrable systems obtained. We discuss the relations
between conservation laws for systems belonging to the Lax-Darboux scheme.Comment: 26 page
On a realization of -expansion in QCD
We suggest a simple algebraic approach to fix the elements of the -expansion for renormalization group invariant quantities, which uses
additional degrees of freedom. The approach is discussed in detail for NLO
calculations in QCD with the MSSM gluino -- an additional degree of freedom. We
derive the formulae of the -expansion for the nonsinglet Adler
-function and Bjorken polarized sum rules in the actual NLO within this
quantum field theory scheme with the MSSM gluino and the scheme with the second
additional degree of freedom. We discuss the properties of the -expansion for higher orders considering the NLO as an example.Comment: 14 pages, Introduction, Sec.2, Conclusion are significantly improve
Endpoint behavior of the pion distribution amplitude in QCD sum rules with nonlocal condensates
Starting from the QCD sum rules with nonlocal condensates for the pion
distribution amplitude, we derive another sum rule for its derivative and its
"integral" derivatives---defined in this work. We use this new sum rule to
analyze the fine details of the pion distribution amplitude in the endpoint
region . The results for endpoint-suppressed and flat-top (or
flat-like) pion distribution amplitudes are compared with those we obtained
with differential sum rules by employing two different models for the
distribution of vacuum-quark virtualities. We determine the range of values of
the derivatives of the pion distribution amplitude and show that
endpoint-suppressed distribution amplitudes lie within this range, while those
with endpoint enhancement---flat-type or CZ-like---yield values outside this
range.Comment: 20 pages, 10 figures, 1 table, conclusions update
Integrable ODEs on Associative Algebras
In this paper we give definitions of basic concepts such as symmetries, first
integrals, Hamiltonian and recursion operators suitable for ordinary
differential equations on associative algebras, and in particular for matrix
differential equations. We choose existence of hierarchies of first integrals
and/or symmetries as a criterion for integrability and justify it by examples.
Using our componentless approach we have solved a number of classification
problems for integrable equations on free associative algebras. Also, in the
simplest case, we have listed all possible Hamiltonian operators of low order.Comment: 19 pages, LaTe
Nonabelian strings in a dense matter
We consider gauge theories with scalar matter with and without supersymmetry
at nonzero chemical potential. It is argued that a chemical potential plays a
role similar to the FI term. We analyze theory at weak coupling regime at large
chemical potential and argue that it supports nonabelian non-BPS strings.
Worldsheet theory on the nonabelian string in a dense matter is briefly
discussed.Comment: 14 page
Perturbative Symmetry Approach
Perturbative Symmetry Approach is formulated in symbolic representation.
Easily verifiable integrability conditions of a given equation are constructed
in the frame of the approach. Generalisation for the case of non-local and
non-evolution equations is disscused. Application of the theory to the
Benjamin-Ono and Camassa-Holm type equations is considered.Comment: 16 page
Cut moments and a generalization of DGLAP equations
We elaborate a cut (truncated) Mellin moments (CMM) approach that is
constructed to study deep inelastic scattering in lepton-hadron collisions at
the natural kinematic constraints. We show that generalized CMM obtained by
multiple integrations of the original parton distribution as well
as ones obtained by multiple differentiations of this also satisfy
the DGLAP equations with the correspondingly transformed evolution kernel
. Appropriate classes of CMM for the available experimental kinematic
range are suggested and analyzed. Similar relations can be obtained for the
structure functions , being the Mellin convolution , where
is the coefficient function of the process.Comment: 11 page
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