5 research outputs found
Magnetization waves in Landau-Lifshitz Model
The solutions of the Landau-Lifshitz equation with finite-gap behavior at
infinity are considered. By means of the inverse scattering method the
large-time asymptotics is obtained.Comment: AmSTeX, Ver. 2.1h, 5 pages, amsppt style, 1 figur
Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data
We consider the one-dimensional focusing nonlinear Schr\"odinger equation
(NLS) with a delta potential and even initial data. The problem is equivalent
to the solution of the initial/boundary problem for NLS on a half-line with
Robin boundary conditions at the origin. We follow the method of Bikbaev and
Tarasov which utilizes a B\"acklund transformation to extend the solution on
the half-line to a solution of the NLS equation on the whole line. We study the
asymptotic stability of the stationary 1-soliton solution of the equation under
perturbation by applying the nonlinear steepest-descent method for
Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens,
and extends, earlier work on the problem by Holmer and Zworski
Classical/quantum integrability in AdS/CFT
We discuss the AdS/CFT duality from the perspective of integrable systems and
establish a direct relationship between the dimension of single trace local
operators composed of two types of scalar fields in N=4 super Yang-Mills and
the energy of their dual semiclassical string states in AdS(5) X S(5). The
anomalous dimensions can be computed using a set of Bethe equations, which for
``long'' operators reduces to a Riemann-Hilbert problem. We develop a unified
approach to the long wavelength Bethe equations, the classical ferromagnet and
the classical string solutions in the SU(2) sector and present a general
solution, governed by complex curves endowed with meromorphic differentials
with integer periods. Using this solution we compute the anomalous dimensions
of these long operators up to two loops and demonstrate that they agree with
string-theory predictions.Comment: 49 pages, 5 figures, LaTeX; v2: complete proof of the two-loop
equivalence between the sigma model and the gauge theory is added. References
added; v4,v5,v6: misprints correcte
On the Convexity of the KdV Hamiltonian
We prove that the nonlinear part H 17 of the KdV Hamiltonian Hkdv, when expressed in action variables I=(In)n 651, extends to a real analytic function on the positive quadrant \u21132+(N) of \u21132(N) and is strictly concave near 0. As a consequence, the differential of H 17 defines a local diffeomorphism near 0 of \u21132C(N)