Search results for "Integrable systems"
showing 10 items of 256 documents
Riemann theta functions, Fredholm and wronskian representations of the solutions to the KdV equation
2021
We degenerate the finite gap solutions of the KdV equation from the general formulation given in terms of abelian functions when the gaps tends to points, to get solutions to the KdV equation given in terms of Fredholm determinants and wronskians. For this we establish a link between Riemann theta functions, Fredholm determinants and wronskians. This gives the bridge between the algebro-geometric approach and the Darboux dressing method.
2N+1 highest amplitude of the modulus of the N-th order AP breather and other 2N-2 parameters solutions to the NLS equation
2015
We construct here new deformations of the AP breather (Akhmediev-Peregrine breather) of order N (or AP N breather) with 2N −2 real parameters. Other families of quasi-rational solutions of the NLS equation are obtained. We evaluate the highest amplitude of the modulus of AP breather of order N ; we give the proof that the highest amplitude of the AP N breather is equal to 2N + 1. We get new formulas for the solutions of the NLS equation, different from these already given in previous works. New solutions for the order 8 and their deformations according to the parameters are explicitly given. We get the triangular configurations as well as isolated rings at the same time. Moreover, the appea…
Families of solutions to the CKP equation with multi-parameters
2020
We construct solutions to the CKP (cylindrical Kadomtsev-Petviashvili)) equation in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions are called solutions of order N ; they depend on 2N − 1 parameters. They can be written as a quotient of 2 polynomials of degree 2N (N + 1) in x, t and 4N (N + 1) in y depending on 2N − 2 parameters. We explicitly construct the expressions up to order 5 and we study the patterns of their modulus in plane (x, y) and their evolution according to time and parameters.
Measurement of the top quark mass in the dilepton channel
2007
We present a measurement of the top quark mass in the dilepton channel based on approximately 370/pb of data collected by the D0 experiment during Run II of the Fermilab Tevatron collider. We employ two different methods to extract the top quark mass. We show that both methods yield consistent results using ensemble tests of events generated with the D0 Monte Carlo simulation. We combine the results from the two methods to obtain a top quark mass m_t = 178.1 +/- 8.2 GeV. The statistical uncertainty is 6.7 GeV and the systematic uncertainty is 4.8 GeV.
Thermodynamics of Toda lattice models: application to DNA
1993
Abstract Our generalised Bethe ansatz method is used to formulate the statistical mechanics of the classical Toda lattice in terms of a set of coupled integral equations expressed in terms of appropriate action-angle variables. The phase space as coordinatised by these action-angle variables is constrained; and both the soliton number density and the soliton contribution to the free energy density can be shown to decouple from the phonon degrees of freedom and to depend only on soliton-soliton interactions. This makes it possible to evaluate the temperature dependence of the soliton number density which, to leading order, is found to be proportional to T 1 3 .
The Peregrine soliton in nonlinear fibre optics
2010
International audience; The Peregrine soliton is a localized nonlinear structure predicted to exist over 25 years ago, but not so far experimentally observed in any physical system. It is of fundamental significance because it is localized in both time and space, and because it defines the limit of a wide class of solutions to the nonlinear Schrödinger equation (NLSE). Here, we use an analytic description of NLSE breather propagation to implement experiments in optical fibre generating femtosecond pulses with strong temporal and spatial localization, and near-ideal temporal Peregrine soliton characteristics. In showing that Peregrine soliton characteristics appear with initial conditions th…
Polarization modulation instability in a Manakov fiber system
2015
International audience; The Manakov model is the simplest multicomponent model of nonlinear wave theory: It describes elementary stable soliton propagation and multisoliton solutions, and it applies to nonlinear optics, hydrodynamics, and Bose-Einstein condensates. It is also of fundamental interest as an asymptotic model in the context of the widely used wavelength-division-multiplexed optical fiber transmission systems. However, although its physical relevance was confirmed by the experimental observation of Manakov (vector) solitons in a planar waveguide in 1996, there have in fact been no quantitative experiments confirming its validity for nonlinear dynamics other than soliton formatio…
Peregrine soliton generation and breakup in standard telecommunications fiber
2011
International audience; We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of non-ideal initial conditions is studied through direct cut back measurements of the longitudinal evolution of the emerging soliton dynamics, and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.
"Table 2" of "Comprehensive measurements of $t$-channel single top-quark production cross sections at $\sqrt{s} = 7$ TeV with the ATLAS detector"
2021
Detailed list of the contribution of each source of uncertainty to the total uncertainty on the measured values of $\sigma(tq)$, $\sigma(\bar{t}q)$, $R_t$, and $\sigma(tq+\bar{t}q)$. The evaluation of the systematic uncertainties has a statistical uncertainty of $0.3\,\%$. Uncertainties contributing less than $1.0\,\%$ are marked with "$<1$" in the paper. To provide numerical values for this table in HEPdata, these uncertainties are approximated with $\pm 0.5\,\%$. This approximation is applied to all measurements for the following uncertainties$:$ JES statistical, JES physics modeling, JES mixed detector and modeling, JES close-by-jets, JES pileup, $b$-JES, jet vertex fraction, mistag e…
"Table 4" of "Comprehensive measurements of $t$-channel single top-quark production cross sections at $\sqrt{s} = 7$ TeV with the ATLAS detector"
2021
Parametrization factors for the $m_{t}$ dependence [see Eq. (4) in the paper] of $\sigma(tq)$, $\sigma(\bar tq)$, and $\sigma(t q+\bar t q)$.