279 research outputs found
A new two-dimensional lattice model that is "consistent around a cube"
For two-dimensional lattice equations one definition of integrability is that
the model can be naturally and consistently extended to three dimensions, i.e.,
that it is "consistent around a cube" (CAC). As a consequence of CAC one can
construct a Lax pair for the model. Recently Adler, Bobenko and Suris conducted
a search based on this principle and certain additional assumptions. One of
those assumptions was the "tetrahedron property", which is satisfied by most
known equations. We present here one lattice equation that satisfies the
consistency condition but does not have the tetrahedron property. Its Lax pair
is also presented and some basic properties discussed.Comment: 8 pages in LaTe
A constructive approach to the soliton solutions of integrable quadrilateral lattice equations
Scalar multidimensionally consistent quadrilateral lattice equations are
studied. We explore a confluence between the superposition principle for
solutions related by the Backlund transformation, and the method of solving a
Riccati map by exploiting two kn own particular solutions. This leads to an
expression for the N-soliton-type solutions of a generic equation within this
class. As a particular instance we give an explicit N-soliton solution for the
primary model, which is Adler's lattice equation (or Q4).Comment: 22 page
An integrable multicomponent quad equation and its Lagrangian formulation
We present a hierarchy of discrete systems whose first members are the
lattice modified Korteweg-de Vries equation, and the lattice modified
Boussinesq equation. The N-th member in the hierarchy is an N-component system
defined on an elementary plaquette in the 2-dimensional lattice. The system is
multidimensionally consistent and a Lagrangian which respects this feature,
i.e., which has the desirable closure property, is obtained.Comment: 10 page
Solutions of Adler's lattice equation associated with 2-cycles of the Backlund transformation
The BT of Adler's lattice equation is inherent in the equation itself by
virtue of its multidimensional consistency. We refer to a solution of the
equation that is related to itself by the composition of two BTs (with
different Backlund parameters) as a 2-cycle of the BT. In this article we will
show that such solutions are associated with a commuting one-parameter family
of rank-2 (i.e., 2-variable), 2-valued mappings. We will construct the explicit
solution of the mappings within this family and hence give the solutions of
Adler's equation that are 2-cycles of the BT.Comment: 10 pages, contribution to the NEEDS 2007 proceeding
Is the Glass Half-empty or Half Full? An Analysis of Agricultural Production Trends in Zambia
This policy brief highlights some of the key trends in Zambia agricultural production since the implementation of partial agricultural reform.food security, food policy, Zambia, agricultural production, Farm Management, Q18,
Is the Glass Half-Empty or Half Full? An Analysis of Agricultural Production Trends in Zambia
One objective of this paper is to examine the trends and changes in crop production before and after the implementation of the partial market liberalization policies starting in the early 1990s. Another objective of the paper is to assess agricultural production performance and its implications for household food security. These issues are examined on the basis of the Crop Forecast Survey (CFS) data, Post Harvest Survey (PHS) data, Central Statistical Office (CSO) price data, data from the Agricultural Market Information Centre (AMIC) at the Ministry of Agriculture, Food and Fisheries (MAFF), and other data.food security, food policy, Zambia, crop production, Crop Production/Industries, Q18,
Markets Need Predictable Government Actions to Function Effectively: The Case of Importing Maize in Times of Deficit
Food relief for vulnerable groups is important in times of deficit. For the remainder of the population, well functioning grain markets can save lives during times of food shortfalls. This note illustrates how predictable Government behavior in the market can improve markets’ ability to meet the needs of consumers.food security, food policy, Zambia, maize, Agricultural and Food Policy, Marketing, Q18,
An algebraic method of classification of S-integrable discrete models
A method of classification of integrable equations on quad-graphs is
discussed based on algebraic ideas. We assign a Lie ring to the equation and
study the function describing the dimensions of linear spaces spanned by
multiple commutators of the ring generators. For the generic case this function
grows exponentially. Examples show that for integrable equations it grows
slower. We propose a classification scheme based on this observation.Comment: 11 pages, workshop "Nonlinear Physics. Theory and Experiment VI",
submitted to TM
A Super-Integrable Discretization of the Calogero Model
A time-discretization that preserves the super-integrability of the Calogero
model is obtained by application of the integrable time-discretization of the
harmonic oscillator to the projection method for the Calogero model with
continuous time. In particular, the difference equations of motion, which
provide an explicit scheme for time-integration, are explicitly presented for
the two-body case. Numerical results exhibit that the scheme conserves all
the conserved quantities of the (two-body) Calogero model with a
precision of the machine epsilon times the number of iterations.Comment: 22 pages, 5 figures. Added references. Corrected typo
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