P. Deift, A. Its, and X. Zhou. Long-time asymptotics for integrable nonlinear wave equations. Important developments in soliton theory,  Home/Search Document Not in Database Summary Related Articles Check |
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The Nonlinear Schrödinger Equation as Both a PDE and a.. - Cai, McLaughlin.. (Correct)
....In this section we will describe the Riemann Hilbert formulation of the inverse spectral problem for the defocusing NLS equation. Then we will use this formulation to establish long time asymptotics for the defocusing NLS equation. The results described here are due to Deift, Its, and Zhou [45]. A more detailed description of the analysis contained in [45] is presented in [53] 7.1 Statement of the Riemann Hilbert Problem Before defining the Riemann Hilbert problem, we begin with an auxiliary matrix valued function: Given a function r( 2 S(R) the Schwarz space of C 1 functions ....
....of the inverse spectral problem for the defocusing NLS equation. Then we will use this formulation to establish long time asymptotics for the defocusing NLS equation. The results described here are due to Deift, Its, and Zhou [45] A more detailed description of the analysis contained in [45] is presented in [53] 7.1 Statement of the Riemann Hilbert Problem Before defining the Riemann Hilbert problem, we begin with an auxiliary matrix valued function: Given a function r( 2 S(R) the Schwarz space of C 1 functions which decay faster than any power as jj 1, we build a matrix v ....
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P. Deift, A. Its, and X. Zhou. Long-time asymptotics for integrable nonlinear wave equations. Important developments in soliton theory,
On the Distribution of the Length of the Longest.. - Baik, Deift, Johansson (1999) (37 citations) Self-citation (Deift) (Correct)
....factors as in (1. 26) This method was further extended in [DVZ1] and eventually placed in a very general form by Deift, Zhou and Venakides in [DVZ2] making possible the analysis of the limiting behavior of a large variety of asymptotic problems in pure and applied mathematics (see, e.g. [DIZ]) As we will see, the application of this method to (1.26) makes it possible to control the large k; behavior of 2 k ( The calculation in this paper have many similarities to the computations in [DKMVZ] where the authors use the steepest descent method to obtain Plancherel Rotach type ....
P.A.Deift, A.R.Its and X.Zhou, Long-time Asymptotics for Integrable Nonlinear Wave Equations, in Important Development in Soliton Theory, 2nd Edition, edited by A.S.Fokas and V.E.Zakharov, Springer-Verlag, to be published.
Differential Equation for a Correlation Function of the.. - Frahm, Its, al. Self-citation (Its) (Correct)
....equations. The Riemann Hilbert problem also provides an adequate parametrization of the space of the solutions for integro difference equations. It sould be noted that just this type of parametrization is most suitable for the asymptotic analysis of the integrable systems (see review paper [6]) This means that quantum correlation function is a function (in a sense of [7] of these integrodifference equations. In order to define the correlation function that we are interested in we introduce the operators P j = 1 2 (oe z j 1) 0 B 1 0 0 0 1 C A ; 1.3) projecting onto the ....
P. A. Deift, A. R. Its, and X. Zhou, "Long-time asymptotics for integrable nonlinear wave equations", in Important Developments in Soliton Theory, edited by A. S. Fokas and V. E. Zakharov, Springer Verlag, Berlin, 1993.
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