منابع مشابه
Jacobi Operators and Completely Integrable Nonlinear Lattices
This book is intended to serve both as an introduction and a reference to spectral and inverse spectral theory of Jacobi operators (i.e., second order symmetric difference operators) and applications of these theories to the Toda and Kac-van Moerbeke hierarchy. Starting from second order difference equations we move on to self-adjoint operators and develop discrete Weyl-Titchmarsh-Kodaira theor...
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Geometrical optics limit of the Maxwell equations for nonlinear media with the Cole-Cole dependence of dielectric function and magnetic permeability on the frequency is considered. It is shown that for media with slow variation along one axis such a limit gives rise to the dispersionless Veselov-Novikov equation for the refractive index. It is demonstrated that the Veselov-Novikov hierarchy is ...
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We introduce a Hodge operator in a framework of noncommutative geometry. The complete integrability of 2-dimensional classical harmonic maps into groups (σ-models or principal chiral models) is then extended to a class of ‘noncommutative’ harmonic maps into matrix algebras.
متن کاملCompletely Integrable Gradient Flows
In this paper we exhibit the Toda lattice equations in a double bracket form which shows they are gradient flow equations (on their isospectral set) on an adjoint orbit of a compact Lie group. Representations for the flows are given and a convexity result associated with a momentum map is proved. Some general properties of the double bracket equations are demonstrated, including a discussion of...
متن کامل6 High frequency integrable regimes in nonlocal nonlinear optics
High frequency integrable regimes in nonlocal nonlinear optics. Abstract We consider an integrable model which describes light beams propagating in nonlocal nonlinear media of Cole-Cole type. The model is derived as high frequency limit of both Maxwell equations and the nonlocal nonlinear Schrödinger equation. We demonstrate that for a general form of nonlinearity there exist selfguided light b...
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ژورنال
عنوان ژورنال: Pramana
سال: 2001
ISSN: 0304-4289,0973-7111
DOI: 10.1007/s12043-001-0008-x