61 research outputs found
Symmetrically coupled higher-order nonlinear Schroedinger equations: singularity analysis and integrability
The integrability of a system of two symmetrically coupled higher-order
nonlinear Schr\"{o}dinger equations with parameter coefficients is tested by
means of the singularity analysis. It is proven that the system passes the
Painlev\'{e} test for integrability only in ten distinct cases, of which two
are new. For one of the new cases, a Lax pair and a multi-field generalization
are obtained; for the other one, the equations of the system are uncoupled by a
nonlinear transformation.Comment: 12 pages, LaTeX2e, IOP style, final version, to appear in
J.Phys.A:Math.Ge
The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities
In this paper, we present extraordinary algebraic and geometrical structures
for the Hunter-Saxton equation: infinitely many commuting and non-commuting
-independent higher order symmetries and conserved densities. Using a
recursive relation, we explicitly generate infinitely many higher order
conserved densities dependent on arbitrary parameters. We find three Nijenhuis
recursion operators resulting from Hamiltonian pairs, of which two are new.
They generate three hierarchies of commuting local symmetries. Finally, we give
a local recursion operator depending on an arbitrary parameter.
As a by-product, we classify all anti-symmetric operators of a definite form
that are compatible with the Hamiltonian operator
On integrability of the vector short pulse equation
Using the Painleve analysis preceded by appropriate transformations of
nonlinear systems under investigation, we discover two new cases in which the
Pietrzyk-Kanattsikov-Bandelow vector short pulse equation must be integrable
due to the results of the Painleve test. Those cases are technologically
important because they correspond to the propagation of polarized ultra-short
light pulses in usual isotropic silica optical fibers.Comment: 10 page
Scalar second order evolution equations possessing an irreducible sl-valued zero curvature representation
We find all scalar second order evolution equations possessing an
sl-valued zero curvature representation that is not reducible to a proper
subalgebra of sl. None of these zero-curvature representations admits a
parameter.Comment: 10 pages, requires nath.st
Integrable quadratic Hamiltonians on so(4) and so(3,1)
We investigate a special class of quadratic Hamiltonians on so(4) and so(3,1)
and describe Hamiltonians that have additional polynomial integrals. One of the
main results is a new integrable case with an integral of sixth degree.Comment: 16 page
Classification of polynomial integrable systems of mixed scalar and vector evolution equations. I
We perform a classification of integrable systems of mixed scalar and vector
evolution equations with respect to higher symmetries. We consider polynomial
systems that are homogeneous under a suitable weighting of variables. This
paper deals with the KdV weighting, the Burgers (or potential KdV or modified
KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings.
The case of other weightings will be studied in a subsequent paper. Making an
ansatz for undetermined coefficients and using a computer package for solving
bilinear algebraic systems, we give the complete lists of 2nd order systems
with a 3rd order or a 4th order symmetry and 3rd order systems with a 5th order
symmetry. For all but a few systems in the lists, we show that the system (or,
at least a subsystem of it) admits either a Lax representation or a linearizing
transformation. A thorough comparison with recent work of Foursov and Olver is
made.Comment: 60 pages, 6 tables; added one remark in section 4.2.17 (p.33) plus
several minor changes, to appear in J.Phys.
Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations
A differential-algebraic approach to studying the Lax type integrability of
the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The
approach is also applied to studying the Lax type integrability of the well
known Korteweg-de Vries dynamical system.Comment: 11 page
Integrable discretizations of derivative nonlinear Schroedinger equations
We propose integrable discretizations of derivative nonlinear Schroedinger
(DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation
and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS
systems admit the reduction of complex conjugation between two dependent
variables and possess bi-Hamiltonian structure. Through transformations of
variables and reductions, we obtain novel integrable discretizations of the
nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS,
matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and
Burgers equations. We also discuss integrable discretizations of the
sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio
МОЛЕКУЛЯРНО-ГЕНЕТИЧЕСКИЙ АНАЛИЗ АЛЛЕЛЬНОГО СОСТАВА СЕЛЕКЦИОННО ЦЕННЫХ ГЕНОВ ОТДАЛЕННЫХ ГИБРИДОВ ТРИТИКАЛЕ
It’s established that 65 separate plants of remote hybrids of spring triticale with wheat of four crossings of generation F4–F5 have allelic composition of genes of grain proteins(Glu-1), dwarfing genes (Rht) and genes controlling vernalization reaction. It’s determined that genes Dx5 and Dy10 of locus Glu-D1 of wheat are transferred to remote hybrids of triticale. Identified are 11 lines of crossing Uzor ç Rostan which are characterized by the optimal composition of all the studied plant breeding valuable genes: Glu-А1b Glu-B1b Glu-D1d on locus Glu-1, Vrn-A1a Vrn-B1а on locus Vrn-1 and Rht-B1b on locus Rht.У 65 индивидуальных растений отдаленных гибридов ярового тритикале с пшеницей четырех комбинаций скрещиваний поколений F4–F5 установлен аллельный состав генов запасных белков зерна (Glu-1), генов карликовости (Rht), а также генов, контролирующих реакцию на яровизацию (Vrn). Выявлено, что гены Dx5 и Dy10 локуса Glu-D1 пшеницы совместно передаются отдаленным гибридам тритикале. Выделено 11 линий комбинации скрещивания Узор ç Ростань, которые характеризуются оптимальным составом всех изученных селекционно ценных генов: Glu-А1b Glu-B1b Glu-D1d по локусу Glu-1, Vrn-A1a Vrn-B1а по локусу Vrn-1 и Rht-B1b по локусу Rht
Large scale analytic calculations in quantum field theories
We present a survey on the mathematical structure of zero- and single scale
quantities and the associated calculation methods and function spaces in higher
order perturbative calculations in relativistic renormalizable quantum field
theories.Comment: 25 pages Latex, 1 style fil
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