Search results for "Integrable system"
showing 10 items of 354 documents
Numerical study of the long wavelength limit of the Toda lattice
2014
We present the first detailed numerical study of the Toda equations in $2+1$ dimensions in the limit of long wavelengths, both for the hyperbolic and elliptic case. We first study the formal dispersionless limit of the Toda equations and solve initial value problems for the resulting system up to the point of gradient catastrophe. It is shown that the break-up of the solution in the hyperbolic case is similar to the shock formation in the Hopf equation, a $1+1$ dimensional singularity. In the elliptic case, it is found that the break-up is given by a cusp as for the semiclassical system of the focusing nonlinear Schr\"odinger equation in $1+1$ dimensions. The full Toda system is then studie…
A numerical study of the small dispersion limit of the Korteweg-de Vries equation and asymptotic solutions
2012
Abstract We study numerically the small dispersion limit for the Korteweg–de Vries (KdV) equation u t + 6 u u x + ϵ 2 u x x x = 0 for ϵ ≪ 1 and give a quantitative comparison of the numerical solution with various asymptotic formulae for small ϵ in the whole ( x , t ) -plane. The matching of the asymptotic solutions is studied numerically.
Asymptotic expansion of a partition function related to the sinh-model
2014
This paper develops a method to carry out the large-$N$ asymptotic analysis of a class of $N$-dimensional integrals arising in the context of the so-called quantum separation of variables method. We push further ideas developed in the context of random matrices of size $N$, but in the present problem, two scales $1/N^{\alpha}$ and $1/N$ naturally occur. In our case, the equilibrium measure is $N^{\alpha}$-dependent and characterised by means of the solution to a $2\times 2$ Riemann--Hilbert problem, whose large-$N$ behavior is analysed in detail. Combining these results with techniques of concentration of measures and an asymptotic analysis of the Schwinger-Dyson equations at the distributi…
Order and Chaos in the Statistical Mechanics of the Integrable Models in 1+1 Dimensions
1991
This paper was presented at the meeting under this title. But, originally, the more cumbersome ‘Quantum chaos — classical chaos in k-space: thermodynamic limits for the sine-Gordon models’ was proposed. Certainly this covers more technically the content of this paper.
"Table 1" of "Search for a heavy top-quark partner in final states with two leptons with the ATLAS detector at the LHC"
2012
(1) Number of generated MC events for the scalar top signal grid (2) Relative Cross section uncertainties for the scalar top signal grid.
"Table 1" of "Measurement of the t anti-t production cross-section in p anti-p collisions using dilepton events"
2008
TOP TOPBAR production cross section for top quark mass 175 GeV.
"Table 1" of "Measurement of the t anti-t production cross section in p anti-p collisions at s**(1/2) = 1.96-TeV"
2008
The combined result for the TOP TOPBAR production cross section at top quark mass of 175 GeV.. The second DSYS error is the uncertainty on the luminosity.
"Table 2" of "Measurement of the t anti-t production cross section in p anti-p collisions at s**(1/2) = 1.96-TeV"
2008
The cross section for TOP TOPBAR production at the world average top quark mass of 172.6 GeV.. Errors contain both statistics and systematics.
"Table 12" of "Search for light scalar top quark pair production in final states with two leptons with the ATLAS detector in sqrt(s) = 7 TeV proton-p…
2012
Distribution of the Jet Multiplicity for all events in the Top Control Region.
"Table 1" of "t anti-t production cross-section in p anti-p collisions at s**(1/2) = 1.8-TeV"
2002
Measured top quark pair production cross section in the different channels and the various averages, including the overall average.