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Saturday, May 9, 2020 | History

6 edition of Hydrodynamics of Soliton Lattices found in the catalog.

Hydrodynamics of Soliton Lattices

by B. Dubrovin

  • 345 Want to read
  • 29 Currently reading

Published by Routledge .
Written in English

    Subjects:
  • Miscellaneous Items,
  • Science / Physics

  • Edition Notes

    SeriesSoviet Scientific Reviews Series, Section C
    The Physical Object
    FormatPaperback
    Number of Pages136
    ID Numbers
    Open LibraryOL12860416M
    ISBN 103718654547
    ISBN 109783718654543

    Purchase Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume - 1st Edition. Print Book & E-Book. ISBN ,   Soliton theory of two-dimensional lattices: the discrete nonlinear schrödinger equation. Arévalo E(1). Author information: (1)Technische Universität Darmstadt, Institut für Theorie elektromagnetischer Felder, TEMF, Schlossgartenstrasse 8 D Darmstadt, by:

    Nevertheless, there are important exceptions, such as the famous Korteweg-de Vries equation and the nonlinear Schr"odinger equation; the term "soliton" refers to certain solutions of such equations. The exact solvability of such equations has been explained by unexpected relations to highly structured mathematical objects such as Riemann. 1 Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices Hector Martin1, Eugenia D. Eugenieva2 and Zhigang Chen1,3 1 Department of Physics and Astronomy, San Francisco State University, CA 2 Intel Corporation, USA, 3 TEDA College, Nankai University, China [email protected] Demetrios N. Christodoulides.

    3. Nonlinear analogue of the WKB-method. Hydrodynamics of Soliton Lattices. Special analysis for the KdV equation. Dispersive analogue of the shock wave. Genus 1 .   Sphere Packings, Lattices and Groups book. Read reviews from world’s largest community for readers. The third edition of this definitive and popular book 5/5.


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Hydrodynamics of Soliton Lattices by B. Dubrovin Download PDF EPUB FB2

The theory of the integrability of hydrodynamic- type systems is presented. Applications of the formalism developed to problems of the hydrodynamics of weakly deformed soliton lattices - slow modulations of families of periodic and quasiperiodic solutions of nonlinear evolution systems, are described.

Novikov S.P. () Differential Geometry and Hydrodynamics of Soliton Lattices. In: Fokas A.S., Zakharov V.E. (eds) Important Developments in Soliton Theory. Springer Series in Nonlinear by: 4.

Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory Article (PDF Available) in Russian Mathematical Surveys 44(6) December with 84 Reads.

Hydrodynamics of weakly deformed soliton lattices 39 A functional of hydrodynamic type I[u(x)] is a quantity whose density is independent of derivatives, (7) I [u] = $/ (u)dx. Definition. Poisson brackets of hydrodynamic type are local Poisson brackets of the form. CONTENTS Introduction Chapter I.

Hamiltonian theory of systems of hydrodynamic type § 1. General properties of Poisson brackets § 2. Hamiltonian formalism of systems of hydrodyn. Solitons in Nonlinear Lattices. Yaroslav V. Kartashov,1 Boris A. Malomed,2 and Lluis Torner1 1ICFO-Institut de Ciencies Fotoniques, and Universitat Politecnica de Catalunya, Medi- terranean Technology Park, Castelldefels (Barcelona), Spain.

2Department of Physical Electronics, School of Electrical Engineering, Faculty of Engi- neering, Tel Aviv University, Tel Aviv,IsraelCited by: E.A. Kuznetsov etal., Soliton stability in plasmas and hydrodynamics Among conservative systems we are interested in systems possessing a Hamiltonian structure.

It should be noted that for conservative systems Hamiltonian structure, as a rule, can be introduced in spite of the fact that there are no general methods of its introduction.

Important Developments in Soliton Theory. Propagation of Oscillations in Dispersive Initial Value Problems and Their Limiting Behavior --Differential Geometry Hydrodynamics of Soliton Lattices --Bi-Hamiltonian Structures and Integrability --On the Symmetries (the connection of the KdV with matrix models).

This is the first book to. This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices.

A majority of the results obtained, thus far, in this field and reviewed in this article are Cited by: Classical analogue of the Dirac monopole, complete integrability and algebraic geometry; 4.

Poisson structures on loop spaces, systems of hydrodynamic type and differential geometry; 5. Non-linear WKB method, hydrodynamics of weakly deformed soliton lattices; References.

Series Title: Lezioni fermiane. Responsibility: S.P. Novikov. More. based on Joseph Boussinesq and Lord Ray leigh ’s enhancements of classical hydrodynamics. 'Soliton Nature' book https: periodic atomic and cell lattices, Lego-like constructions, quanta Author: Sergei Eremenko.

Lattices, SVP and CVP, have been intensively studied for more than years, both as intrinsic mathemati-cal problems and for applications in pure and applied mathematics, physics and cryptography.

The theoretical study of lattices is often called the Geometry of Numbers, a name bestowed on it by Minkowski in his book Geometrie der Size: KB.

In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones.

The text is a self-contained, comprehensive introduction to the theory of hydrodynamic lattice gases. Lattice-gas cellular automata are discrete models of fluids. Identical particles hop from site to site on a regular lattice, obeying simple conservative scattering rules when they collide.

Remarkably, at a scale larger than the lattice spacing, these discrete models simulate the Navier-Stokes. 13 Solitons and Charge Transport in Triangular and Quadratic Crystal Lattices ρ(x,y,t) = ρ0sech2(κξ), ξ = (x ±vst)/σ, () where vs is the soliton velocity.

The soliton represented by () is a special solu-File Size: 8MB. Soliton trains in photonic lattices. Kartashov Y, Vysloukh V, Torner L. We address the formation and propagation of multi-spot soliton packets in saturable Kerr nonlinear media with an imprinted harmonic transverse modulation of the refractive index.

We show that, in sharp contrast to homogeneous media where stable multi-peaked solitons do not Cited by: procedure was used to analyze soliton stability and obtain perturbation growth rates δ.

For focusing nonlinearity optical lattices support two types of lowest order solitons: odd an even (Fig.

Maximum of odd soliton coincides with the maximum of R(η) (Fig. 1(c)), while even one is centered between neighboring maximums of R(η) (Fig. 1(d. Physica D 68 () North-Holland SDI: (93)E Solitons on lattices D.B.

Duncan, J.C. Eilbeck, H. Feddersen and J.A.D. Wattis Department of Mathematics, Heriot-Watt University, Edinburgh, EHl4 4AS, UK RMICA We examine a variety of numerical and approximate analytical methods to study families of solitary waves on by: A theory is developed which describes the slow time and space evolution of a sine-Gordon soliton lattice, taking dissipation into account.

The theory Cited by: 2. About this book This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum.

This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons that satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the File Size: 7MB.The lattice consists of two interpenetrating face centered cubic lattices.

[the structure of NaCl]. The lattice of sites organizes a chain complex L of four vector spaces built from overlapping uniform cubes, faces, edges and sites giving a multilayered covering of periodic three space.Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices.

When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A, which are unexpectedly good and very