Last edited by Kazrashakar
Saturday, July 25, 2020 | History

6 edition of KdV & KAM found in the catalog.

# KdV & KAM

## by Thomas Kappeler

Written in English

Subjects:
• Korteweg-de Vries equation,
• Hamiltonian systems,
• Boundary value problems,
• Perturbation (Mathematics)

• Edition Notes

Includes bibliographical references (p. [267]-273) and index.

Classifications The Physical Object Other titles KdV and KAM. Statement Thomas Kappeler, Jürgen Pöschel. Series Ergebnisse der Mathematik und ihrer Grenzgebiete -- 3. Folge, v. 45., Ergebnisse der Mathematik und ihrer Grenzgebiete -- 3. Folge, Bd. 45. Contributions Pöschel, Jürgen. LC Classifications QA377 .K363 2003, QA377 .K363 2003 Pagination xii, 279 p. : Number of Pages 279 Open Library OL17722571M ISBN 10 3540022341 LC Control Number 2003052621

Abstract. In this note we give an overview of results concerning the Korteweg-de Vries equation ut=uxxx+6uux\ud and small perturbations of it. All the technical details are contained in our book [KdV & KAM, Springer, Berlin, MR]. \ud The KdV equation is an evolution equation in one space dimension which is named after the two Dutch mathematicians Korteweg and de Vries, but was. The book under review provides all the tools leading to the complete solution [KP03] ThomasKappelerandJ¨urgenP¨oschel,KdV & KAM,ErgebnissederMathematikund ihrer Grenzgebiete Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathe-.

Book Search tips Selecting this option will search all publications across the Scitation platform Selecting this option will search all publications for the Publisher/Society in context. “ KAM tori for higher dimensional beam equations with constant potentials,” Nonlinear KdV & KAM, (Springer, ). 《KdV方程和KAM理论(影印版)》介绍了可积偏微分方程理论的两个方面。第一个方面是可积偏微分方程的正规形式理论，以很重要的非线性可积偏微分方程——周期的Korteweg de Vries方程为例来阐述这个正规形式理论，这构成了书的“KdV”部分。.

KdV & KAM(Reprint) (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) by Thomas Kappeler, Jürgen Pöschel, Jurgen Poschel, Jãœrgen PãSchel Paperback, Pages, Published by Springer ISBN , ISBN: In this paper, we investigate one-dimensional generalized Benjamin-Ono equation, \begin{eqnarray} u_t+\mathcal{H}u_{xx}+u^{4}u_x=0,x\in\mathbb{T}, \end{eqnarray} and prove the existence of quasi-periodic solutions with two frequencies. The proof is based on partial Birkhoff normal form and an unbounded KAM theorem developed by Liu-Yuan[()].

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"In this elegantly written book, the authors approach two essential facets of the Hamiltonian PDEs theory. the results stated in the book are exposed in a very clear and pedagogical way and they provide a quite complete picture of the two subjects: ‘Kdv’ and ‘KAM’.

the illuminating overview and the introductions of each. KdV & KAM by Thomas Kappeler,available at Book Depository with free delivery worldwide. Perturbed KdV equations The main KdV & KAM book Birkhoff normal form Global coordinates and frequencies The KAM theorem Proof of the main theorems --V.

The KAM proof Set up and summary of main results The linearized equation The KAM step Iteration and convergence The excluded set of. KdV & KAM | Thomas Kappeler, Jürgen Pöschel | download | B–OK. Download books for free.

Find books. This text treats the Korteweg-de Vries (KdV) equation with periodic boundary conditions. This equation models waves in homogeneous, weakly nonlinear and weakly dispersive media in general.

For the first time, these important results are comprehensively covered in book form, authored by internationally renowned experts in the field. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this note we give an overview of results concerning the Korteweg-deVries equation ut = −uxxx + 6uux and small perturbations of it.

All the technical details will be contained in our forth-coming book [27]. The KdV equation is an evolution equation in one space dimension which is named after the two Dutch. In this text the authors consider the Korteweg-de Vries (KdV) equation (u t = - u xxx + 6uu x) with periodic boundary d to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in.

In this note we give an overview of results concerning the Korteweg-de Vries equation ut=uxxx+6uux and small perturbations of it. All the technical details are contained in our book [KdV & KAM.

Thomas Kappeler's 98 research works with citations and 2, reads, including: On efficiency and localisation for the torsion function. In mathematics, the Korteweg–de Vries (KdV) equation is a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an exactly solvable model, that is, a non-linear partial differential equation whose solutions can be exactly and precisely specified.

KdV can be solved by means of the inverse scattering transform. "In this elegantly written book, the authors approach two essential facets of the Hamiltonian PDEs theory. the results stated in the book are exposed in a very clear and pedagogical way and they provide a quite complete picture of the two subjects: ‘Kdv’ and ‘KAM’.

the illuminating overview and the introductions of each Price: $The first KAM results for KdV have been proved by Kuksin, and then by Kappeler and Pöschel, for semilinear Hamiltonian perturbations ε ∂ x (∂ u f) (x, u), namely when the density f is independent of u x, so that is a differential operator of order 1. The KAM theorems in, prove the persistence of the finite-gap solutions of the integrable KdV under semilinear Hamiltonian perturbations ε ∂ x (∂ u f) (x, u), namely when the density f is independent of u x, so that is a differential operator of order 1 (note that in such nonlinearities are called “quasi-linear” and “strongly. Get this from a library. KdV & KAM. [Thomas Kappeler; Jürgen Pöschel] -- In this text the authors consider the Korteweg-de Vries (KdV) equation (ut = - uxxx + 6uux) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel. KAM Theory THOMAS KAPPELER &JURGEN¨ POSCHEL¨ In this note we give an overview of results concerning the Korteweg-de Vries equation ut =−uxxx +6uux and small perturbations of it. All the technical details will be contained in our forth-coming book [27]. The KdV equation is an evolution equation in one space dimension which is. Rosewill RKV-2UC 2-Port USB KVM Switch.$ off w/ combo purchase, limited offer.

Type: D-Sub, USB Computer Connections: 2 Ports Monitor Connections: 1 Port Video Resolution: x Model #: RKV-2UC Item #: N82E Return Policy: Standard Return Policy One console (monitor, USB keyboard and USB mouse) controls 2 computers. The proof is based on an infinite dimensional KAM Theorem.

American Institute of Mathematical Sciences. KdV & KAM (Ergebnisse der Mathematik und ihrer Grenzgebiete. Folge / A Series of Modern Surveys in Mathematics) (Reprint Edition) by Thomas Kappeler, Jürgen Pöschel, Jurgen Poschel, Jãœrgen PãSchel Paperback, Pages, Published ISBN / ISBN / In this text the authors consider the Korteweg-de Vries (KdV).

This equation models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. For the first time, these important results are comprehensively covered in book form, authored by internationally renowned experts in the field.

Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. Folge /: Kdv & Kam (Paperback). There is a nice recent book H Scott Dumas: The KAM Scientific It does not go very deep but it is, as the subtitle says, a friendly introduction. I guess it might be a beneficial supplementary source in studying the KAM theory as there is a lot of its history and motivation presented.

Russian translation: KdV & KAM, Regular & Chaotic Dynamics, Moscow, Abstract: In this book we consider the Korteweg-de Vries equation u_t=u_xxx+6uu_x with periodic boundary conditions.

Derived as a model equation for long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and.Thomas Kappeler and Jürgen Pöschel, KdV & KAM, Ergebnisse der Mathematik und ihrer Grenzgebiete.

3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol.

45, Springer-Verlag, Berlin, MR In this book we consider the periodic KdV equation as an infinite dimensional integrable Hamiltonian system, and subject it to small Hamiltonian perturbations. To this end, we extend many concepts, ideas and notions from the classical finite dimensional theory, such as angle-action coordinates, Birkhoff normal forms, and in particular KAM theory.