2 edition of **Spectral transform and solitons** found in the catalog.

Spectral transform and solitons

F. Calogero

- 229 Want to read
- 17 Currently reading

Published
**1982**
by North-Holland, Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1982- in Amsterdam, New York, New York
.

Written in English

- Evolution equations, Nonlinear,
- Solitons,
- Spectral theory (Mathematics),
- Transformations (Mathematics)

**Edition Notes**

Includes index. Bibliography: v. 1, p. 488-510.

Series | Studies in mathematics and its applications -- v. 13, Studies in mathematics and its applications -- 13 |

Contributions | Degasperis, Antonio |

The Physical Object | |
---|---|

Pagination | v. 1. : |

ID Numbers | |

Open Library | OL19121367M |

orF a global spectral model, spectral transforms are a combination of a Leg-endre transform and a ourierF transform. A spectral limited-area model like Aladin uses a double ourierF representation for spectral elds. 2 Spectral representation Spherical harmonics The spherical Laplacian operator on a sphere of radius aadmits as. A HERMITE SPECTRAL METHOD FOR SOLITONS boundary conditions, which do not modify the solution is an active ﬁeld of research. The Fourier method uses periodic functions. We must again truncate the domain and impose periodic boundary conditions. In fact, we solve a modiﬁed problem, not the given problem.

The physical phenomena that take place in nature generally have complicated nonlinear features. A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE) as an example. One remarkable feature of the VE is that it possesses loop-like soliton solutions. Loop-like solitons are a class of interesting wave Author: Vyacheslav O. Vakhnenko, E. John Parkes, Dmitri B. Vengrovich. A. Lagg – Spectral Analysis Spectral Analysis and Time Series Andreas Lagg Part I: fundamentals on time series classification prob. density func. autocorrelation power spectral density crosscorrelation applications preprocessing sampling trend removal Part II: Fourier series definition method properties convolution correlations.

5. Fourier Transform and Spectrum Analysis • Although DFT gives exact frequency response of a signal, sometimes it may not give the desired spectrum • Example 0 n 9 N = 10N = 10 x[n] X p(ωˆ) One period of k 10 X[k] if N = 10 So different from X p(ωˆ) Fourier Transform DFTFile Size: KB. Solitons as particles 1 A brief history of topological solitons 3 Bogomolny equations and moduli spaces 7 Soliton dynamics 8 Solitons and integrable systems 10 Solitons – experimental status 12 Outline of this book 14 2Lagrangians and ﬁelds 15 Finite-dimensional systems 15 Symmetries and conservation laws 21File Size: 7MB.

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Spectral Transform and Solitons One (STUDIES IN MATHEMATICS AND ITS APPLICATIONS) (v. 1) by Francesco Calogero (Author), A. Degasperis (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Authors: Francesco Calogero, A.

Degasperis. Purchase Spectral Transform and Solitons, Volume 13 - 1st Edition. Print Book & E-Book. ISBNPages: Solitons: An Introduction discusses the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences.

Drazin and Johnson explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering by: Search in this book series. Spectral Transform and Solitons Tools to Solve and Investigate Nonlinear Evolution Equations. Edited by Francesco Calogero, Antonio Degasperis.

Vol Pages ii-xv, () Download full volume. Previous volume. The spectral transform technique as a method of solving certain classical non linear differential equations was introduced in [], and has played an important role since sly, it uses the formulation (and abstract solution) of a problem known from quantum mechanics, namely that of solving.

Calogero F. () Spectral Transform and Solitons. In: Benedek G., Bilz H., Zeyher R. (eds) Statics and Dynamics of Nonlinear Systems. Springer Series in Solid-State Sciences, vol Cited by: Get this from a library. Spectral transform and solitons: tools to solve Spectral transform and solitons book investigate nonlinear evolution equations.

[Francesco Calogero; Antonio Degasperis]. Devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. Digital Signal Processing/Spectral Transforms.

From Wikibooks, open books for an open world and then using a spectral transform to convert that lowpass filter equation into the equation of a different type of filter. This is done because many common values for butterworth, cheybyshev and elliptical low-pass filters are already extensively.

The book, after giving a short introduction to some mathematical techniques for nonlinear problems, covers related topics such as the history of particle physics; a physical description of the spectral transform; solitons in randomly inhomogenous media; and.

In these cases to any solution u(x, t) one can associate a set of spectral data, the spectral transform, say the analog of the Fourier transform in a nonlinear context. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations.

The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. Solitons in multidimensions: inverse spectral transform method / B.G.

Konopelchenko. This monograph presents the principal ideas, methods and results concerning multidimensional soliton equations. The multidimensional inverse spectral transform method has been developed mainly during the last decade. Solitons and the equations which commonly describe them are also of great mathematical interest.

Thus, the dis covery in and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics.

Discrete spectral incoherent solitons in nonlinear media with noninstantaneous response Article (PDF Available) in Physical Review A 83(2) February with 40 Reads How we measure 'reads'.

Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the fast Fourier idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and then to choose the.

The book, after giving a short introduction to some mathematical techniques for nonlinear problems, covers related topics such as the history of particle physics; a physical description of the spectral transform; solitons in randomly inhomogenous media; and localized wave fields in nonlinear dispersive Edition: 1.

The Spectral Transform Algorithm The spectral transform method is based on a dual representation of the scalar fields in terms of a truncated series of spherical harmonic functions and in terms of values on a rectangular tensor-product grid whose axes represent longitude and latitude.

Spectral transform We are witnessing an explosion of multimedia content, such as music, images, and video, over the internet and in the world of PDAs (personal data assistants) today.

One of the main driving forces behind this phenomenon is the availability of effective. In mathematics, the inverse scattering transform is a method for solving some non-linear partial differential is one of the most important developments in mathematical physics in the past 40 years [citation needed].The method is a non-linear analogue, and in some sense generalization, of the Fourier transform, which itself is applied to solve many linear partial differential.

The Inverse Scattering Transform--Continuous and Discrete and its Relationship with Painlevé Transcendents, M.J. Ablowitz, in Nonlinear Evolution Equations Solvable by the Spectral Transform, ppEd. F. Calogero, Research Notes in Mathemat Pitman, London ().

C–feature space – derived from the image or spectral space Spectral Transforms 4 Fall Feature Spaces •Good features reduce effects that hinder the extraction of information •Nonlinear spectral transform –multispectral ratios are one example •Linear spectral transform –corresponds to a coordinate rotation of the DN space to the File Size: 6MB."A study of the direct spectral transform for the defocusing Davey-Stewartson II equation in the semiclassical limit" has been published in Comm.

Pure Appl. Math. See this paper» "Dispersive asymptotics for linear and integrable equations by the \(\overline{\partial}\) steepest descent method" has been accepted for publication in Fields Inst.