Search results for "Integrable systems"
showing 10 items of 256 documents
On deformation of Poisson manifolds of hydrodynamic type
2001
We study a class of deformations of infinite-dimensional Poisson manifolds of hydrodynamic type which are of interest in the theory of Frobenius manifolds. We prove two results. First, we show that the second cohomology group of these manifolds, in the Poisson-Lichnerowicz cohomology, is ``essentially'' trivial. Then, we prove a conjecture of B. Dubrovin about the triviality of homogeneous formal deformations of the above manifolds.
Integrable systems, Frobenius manifolds and cohomological field theories
2022
In this dissertation, we study the underlying geometry of integrable systems, in particular tausymmetric bi-Hamiltonian hierarchies of evolutionary PDEs and differential-difference equations.First, we explore the close connection between the realms of integrable systems and algebraic geometry by giving a new proof of the Witten conjecture, which constructs the string taufunction of the Korteweg-de Vries hierarchy via intersection theory of the moduli spaces of stable curves with marked points. This novel proof is based on the geometry of double ramification cycles, tautological classes whose behavior under pullbacks of the forgetful and gluing maps facilitate the computation of intersection…
Spectral approach to the scattering map for the semi-classical defocusing Davey–Stewartson II equation
2019
International audience; The inverse scattering approach for the defocusing Davey–Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.
Rational solutions to the KPI equation from particular polynomials
2022
Abstract We construct solutions to the Kadomtsev–Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second spatial derivative of a logarithm of a determinant of order n . We obtain with this method an infinite hierarchy of rational solutions to the KPI equation. We give explicitly the expressions of these solutions for the first five orders.
"Table 2" of "Study of $e^+e^- \rightarrow p\bar{p}$ in the vicinity of $\psi(3770)$"
2014
The two solutions of the dressed cross section and the corresponding phase angles, PHI.
Slow-light soliton dynamics with relaxation
2007
We solved the problem of soliton dynamics in the presence of relaxation. We demonstrate that the spontaneous emission of atoms is strongly suppressed due to nonlinearity. The spatial shape of the soliton is well preserved.
Self-dressing in classical and quantum electrodynamics
2003
A short review is presented of the theory of dressed states in nonrelativistic QED, encompassing fully and partially dressed states in atomic physics. This leads to the concept of the reconstruction of the cloud of virtual photons and of self-dressing. Finally some recent results on the classical counterpart of self-dressing are discussed and a comparison is made with the QED case. Attention is drawn to open problems and future lines of research are briefly outlined.
Statistical Mechanics of the Integrable Models
1987
There is an infinity of classically integrable models. The only ones we can consider here, and these only briefly, are: the sine-Gordon (s-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sin \phi ,$$ (1.1) the sinh-Gordon (sinh-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sinh \phi ,$$ (1.2) and the repulsive and attractive non-linear Schrodinger (NLS) models $${}^ - {\rm{i}}{\phi _{\rm{t}}} = {\phi _{{\rm{xx}}}}{}^ - 2{\rm{c}}\phi {\left| \phi \right|^2}.$$ (1.3) The “attractive” NLS has real coupling constant c 0; φ is complex. In (1.1) and (1.2) m is a mass (ħ = c = 1) and φ is real. These 4 integrable models are in one space and one time …
Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations
1985
We are going to describe our work on the quantum and classical statistical mechanics of some exactly integrable non-linear one dimensional systems. The simplest is the non-linear Schrodinger equation (NLS) $$i{\psi _t} = - {\psi _{XX}} + 2c{\psi ^ + }\psi \psi $$ (1) where c, the coupling constant, is positive. The others are the sine- and sinh-Gordon equations (sG and shG) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi $$ (1.2) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sinh \phi $$ (1.3)
gg→HH : Combined uncertainties
2021
In this paper we discuss the combination of the usual renormalization and factorization scale uncertainties of Higgs-pair production via gluon fusion with the novel uncertainties originating from the scheme and scale choice of the virtual top mass. Moreover, we address the uncertainties related to the top-mass definition for different values of the trilinear Higgs coupling and their combination with the other uncertainties.