2 edition of **The discrete nonlinear Schrödinger equation** found in the catalog.

- 90 Want to read
- 24 Currently reading

Published
**2009**
by Springer in Berlin
.

Written in English

- Nonlinear systems,
- Nonlinear wave equations,
- Schrödinger equation

**Edition Notes**

Includes bibliographical references and index.

Statement | Panayotis G. Kevrekidis ; with contributions by Ricardo Carretero-González ... [et al.]. |

Series | Springer tracts in modern physics -- v. 232 |

Contributions | Carretero-González, Ricardo, SpringerLink (Online service) |

Classifications | |
---|---|

LC Classifications | QC174.26.W28 K48 2009, QC1 .S797 no.232 |

The Physical Object | |

Pagination | xx, 415 p. : |

Number of Pages | 415 |

ID Numbers | |

Open Library | OL25541742M |

ISBN 10 | 3540891986 |

ISBN 10 | 9783540891994, 9783540891987 |

LC Control Number | 2008940668 |

OCLC/WorldCa | 277069173 |

Handbook of exact solutions to the nonlinear Schrödinger equations / Usama Al Khawaja and Laila Al Sakkaf. IOP ebooks. [ collection] Format/Description: Book 1 online resource (various pagings): illustrations (some color). Subjects: Schrödinger equation. Differential equations, Nonlinear. Nonlinear wave equations. System Details. Downloadable (with restrictions)! We find the analytical solutions of the discrete nonlinear Schrödinger equation which models arrays of optical fibers according to the fact that the signal which propagate in the fiber under consideration of the array can be prone to the lateness or accelerating effects of the neighbouring fibers. Firstly, we give the recurrence relation which governs the.

F. Merle, Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys., (), doi: /BF Google Scholar [17] F. Merle and H. Zaag, O.D.E. type behavior of blow-up solutions of nonlinear heat equations, Discrete. The nonlinear Schrödinger equation with wave operator is one of most important nonlinear Schrödinger–type equations, it has been derived from many physical areas. For example, the nonrelativistic limit of the Kelin–Gordon equation [34], [38], [42], the Langmuir wave envelope approximation in plasma [7] and the modulated planar pulse.

We derive a class of discrete nonlinear Schrödinger (DNLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic problem. It is demonstrated that the derived class of discretizations contains subclasses conserving classical norm or a modified norm and classical momentum. These equations are interesting from the physical. Higher dimensional integrable mappings derived from coupled discrete nonlinear Schrödinger equations J. Math. Phys. 50, (); / Cylindrical nonlinear Schrödinger equation versus cylindrical Korteweg‐de Vries equation AIP Conf. Proc. , (); /

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This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes. It contains an introduction to the model, its systematic derivation and its connection to applications, a subsequent analysis of.

The book provides a comprehensive and useful guide to the substantial mathematical and physical literature on the discrete nonlinear Schrödinger equation, both for novices and experts in the field.” (Karsten Matthies, Mathematical Reviews, Issue e) From the Back by: The book provides a comprehensive and useful guide to the substantial mathematical and physical literature on the discrete nonlinear Schrödinger equation, both for novices and experts in the field.” (Karsten Matthies, Mathematical Reviews, Issue e).

The book provides a comprehensive and useful guide to the substantial mathematical and physical literature on the discrete nonlinear Schrödinger equation, both for novices and experts in the field.” (Karsten Matthies, Mathematical Reviews, Issue e)Price: $ The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives Panayotis G.

Kevrekidis (auth.) This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical. The IST The discrete nonlinear Schrödinger equation book applies to continuous and discrete nonlinear Schrödinger (NLS) equations of scalar and vector type.

This work presents a detailed mathematical study of the scattering theory, offers soliton solutions, and analyzes both scalar and vector soliton by: This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource.

In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. View chapter, Discrete Nonlinear Schrödinger Equation PDF chapter.

Salerno equation was extensively analyzed by Hennig and co-workers50 and is also described in the book by Scott Another possible source of confusion is that the acronym DNLS is some-times used for the Derivative Nonlinear Schr˜odinger equation2. The DST equation (4) can be derived from the Hamiltonian: H = Xf j=1 h!(j) 0 jA jj 2 ¡ ° 2 jA.

The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schrödinger-type models that arise therein.

The Defocusing Nonlinear Schrödinger Equation is a broad study of nonlinear excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear. This book has been cited by the following publications.

On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. SIAM J. Appl. Math., 50 (2), – Discrete nonlinear hyperbolic equations: classification of integrable cases. Funktsional. Anal.

i Prilozhen., 43 (1). System Upgrade on Feb 12th During this period, E-commerce and registration of new users may not be available for up to 12 hours.

For online purchase, please visit us again. Integrability test of discrete nonlinear Schrödinger equations via multiscale reduction. Applicable Analysis: Vol. 89, Continuous and Discrete Integrable Systems with Applications, pp.

The IST has been extended to semi-discrete nonlinear ev olution equations (discrete in space and continuous in time) as well as doubly discrete (discrete in both space and time) systems.

The discrete coupled nonlinear Schrödinger (DCNLS) hierarchy associated with a discrete \(3\times 3\) matrix spectral problem is derived, which are composed of the positive and negative flows. Utilizing the characteristic polynomial of Lax matrix for the DCNLS hierarchy, we introduce a trigonal curve with three infinite points and three zero points, from which we establish the associated.

The Discrete Nonlinear Schrödinger Equation 作者: Panayotis G. Kevrekidis 出版社: Springer 副标题: Mathematical Analysis, Numerical Computations and Physical Perspectives (Springer Tracts in Modern Physics) 出版年: 页数: 定价: USD 装帧: Hardcover ISBN: integrable discrete nonlinear Schr odinger equation (focusing) i d dt R n+(R n+1 2R n+R n 1)+jR nj 2(R n+1+R n 1) = 0 Both have solitons: carrier wave (exp, oscillatory) traveling solitary wave (sech) 4.

Integrable discrete NLS (IDNLS) 2 z 1 eigenvalue, jz 1j>1. The system of coupled nonlinear Schrödinger equations (CNLSEs) also termed as the vector Schrödinger equation is a soliton supporting dynamical system.

For the first time, it is considered as a model of light propagation in Kerr isotropic media (see, for example,). Along with that, the phenomenology of the equation opens up the prospect of.

by models of the discrete nonlinear Schrödinger (DNLS) type (i.e., resembling the ﬁnite-difference discretization of the continuum equation) [7, 8].

In that regard, to understand the existence and stability properties of vortices in the. Solitonlike solutions of the generalized discrete nonlinear Schro¨dinger equation D.

Hennig, 1K. Rasmussen,1,2 H. Gabriel, and A. Bu¨low1 1Freie Universita¨t Berlin, Fachbereich Physik, Institut fu¨r Theoretische Physik Arnimal Berlin, Germany 2Institute of Mathematical Modelling, Technical University of Denmark, Anker Engelundsvej, DK Lyngby, Denmark.

The fractional Schrödinger equation is a fundamental equation of fractional quantum was discovered by Nick Laskin () as a result of extending the Feynman path integral, from the Brownian-like to Lévy-like quantum mechanical term fractional Schrödinger equation was.

Thus, the nonlinear Schroedinger equation includes higher-order dispersions and nonlinear optical effects, and accurately reproduces an effect of delayed Raman response. Therefore, by using the nonlinear Schroedinger equation, it is possible to accurately analyze a temporal evolution of ultrashort pulse with a duration of 20~30 fs.The discrete nonlinear Schrödinger equation: mathematical analysis, numerical computations and physical perspectives.

"The collection contains 22 articles on various aspects of the discrete nonlinear Schroedinger equation. The book provides a comprehensive and useful guide to the substantial Read more User-contributed reviews.In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose–Einstein condensates confined to highly anisotropic cigar-shaped traps, in the mean-field regime.