Solutions Of Nonlinear Schr Dinger Systems

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Handbook Of Exact Solutions To The Nonlinear Schrodinger Equations

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Author : Usama Al Khawaja
language : en
Publisher: IOP Publishing Limited
Release Date : 2024-09-30

Handbook Of Exact Solutions To The Nonlinear Schrodinger Equations written by Usama Al Khawaja and has been published by IOP Publishing Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-30 with Science categories.

This book aims to organise and centralise existing solutions of the nonlinear Schrödinger equation (NLSE). This expanded second edition contains new solutions published or derived since the first edition. Noting the increasing interest in and applications of the fractional nonlinear Schrödinger equation, a new chapter devoted to this topic has been added.

Solutions Of Nonlinear Schr Dinger Systems

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Author : Zhijie Chen
language : en
Publisher:
Release Date : 2014-12-31

Solutions Of Nonlinear Schr Dinger Systems written by Zhijie Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-31 with categories.

The Defocusing Nonlinear Schr Dinger Equation

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Author : Panayotis G. Kevrekidis
language : en
Publisher: SIAM
Release Date : 2015-08-04

The Defocusing Nonlinear Schr Dinger Equation written by Panayotis G. Kevrekidis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-04 with Mathematics categories.

Bose?Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose?Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schr?dinger-type models that arise therein. The Defocusing Nonlinear Schr?dinger Equation is a broad study of nonlinear excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schr?dinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.

Nonlinear Systems And Their Remarkable Mathematical Structures

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Author : Norbert Euler
language : en
Publisher: CRC Press
Release Date : 2021-09-07

Nonlinear Systems And Their Remarkable Mathematical Structures written by Norbert Euler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering sciences Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained

Symmetry Analysis And Exact Solutions Of Equations Of Nonlinear Mathematical Physics

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Author : W.I. Fushchich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Symmetry Analysis And Exact Solutions Of Equations Of Nonlinear Mathematical Physics written by W.I. Fushchich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.

by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.

Nearly Integrable Infinite Dimensional Hamiltonian Systems

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Author : Sergej B. Kuksin
language : en
Publisher:
Release Date : 2014-01-15

Nearly Integrable Infinite Dimensional Hamiltonian Systems written by Sergej B. Kuksin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Solitons

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Author : Mohamed Atef Helal
language : en
Publisher: Springer Nature
Release Date : 2022-11-12

Solitons written by Mohamed Atef Helal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-12 with Science categories.

This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.

Numerical And Analytical Solutions For Solving Nonlinear Equations In Heat Transfer

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Author : Ganji, Davood Domiri
language : en
Publisher: IGI Global
Release Date : 2017-07-26

Numerical And Analytical Solutions For Solving Nonlinear Equations In Heat Transfer written by Ganji, Davood Domiri and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Technology & Engineering categories.

Engineering applications offer benefits and opportunities across a range of different industries and fields. By developing effective methods of analysis, results and solutions are produced with higher accuracy. Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer is an innovative source of academic research on the optimized techniques for analyzing heat transfer equations and the application of these methods across various fields. Highlighting pertinent topics such as the differential transformation method, industrial applications, and the homotopy perturbation method, this book is ideally designed for engineers, researchers, graduate students, professionals, and academics interested in applying new mathematical techniques in engineering sciences.

Analytical Methods For Nonlinear Oscillators And Solitary Waves

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Author : Chu-Hui He
language : en
Publisher: Frontiers Media SA
Release Date : 2023-11-24

Analytical Methods For Nonlinear Oscillators And Solitary Waves written by Chu-Hui He and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-24 with Science categories.

The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.

The Nonlinear Schr Dinger Equation

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Author : Catherine Sulem
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06-18

The Nonlinear Schr Dinger Equation written by Catherine Sulem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-18 with Mathematics categories.

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.