[PDF] Handbook Of Exact Solutions To The Nonlinear Schrodinger Equations eBook

Author : Usama Al Khawaja
Publisher : Institute of Physics Publishing
Page : 396 pages
File Size : 19,79 MB
Release : 2019-11-15
Category : Science
ISBN : 9780750324298

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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. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

Author : Usama Al Khawaja
Publisher :
Page : pages
File Size : 24,96 MB
Release : 2019
Category : SCIENCE
ISBN : 9780750324274

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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. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics.

Author : Andrei D. Polyanin
Publisher : CRC Press
Page : 660 pages
File Size : 19,76 MB
Release : 2024-08-26
Category : Mathematics
ISBN : 1040092934

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This reference book describes the exact solutions of the following types of mathematical equations: ● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial Differential Equations ● Linear Equations and Problems of Mathematical Physics ● Nonlinear Equations of Mathematical Physics ● Systems of Partial Differential Equations ● Integral Equations ● Difference and Functional Equations ● Ordinary Functional Differential Equations ● Partial Functional Differential Equations The book delves into equations that find practical applications in a wide array of natural and engineering sciences, including the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and more. Most of these equations are of a reasonably general form and dependent on free parameters or arbitrary functions. The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as to check and compare the effectiveness of exact analytical methods.

Author : Andrei D. Polyanin
Publisher : CRC Press
Page : 835 pages
File Size : 30,91 MB
Release : 2003-10-29
Category : Mathematics
ISBN : 0203489659

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The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types,

Author : Morris, J. Ll. (John Ll.)
Publisher : University of Waterloo, Faculty of Mathematics
Page : 22 pages
File Size : 45,44 MB
Release : 1988
Category : Differential equations, Nonlinear
ISBN :

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Abstract: "Exact solutions of a generalized nonlinear Schrödinger equation [formula] are obtained by transforming the equation to one whose coefficients satisfy a simple algebraic relationship. The transformed equation also yields conservation laws and sufficient conditions for boundedness and blow-up of solutions for the original equation."

Author : Victor A. Galaktionov
Publisher : CRC Press
Page : 530 pages
File Size : 15,3 MB
Release : 2006-11-02
Category : Mathematics
ISBN : 1420011626

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Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book

Author : Peter E. Zhidkov
Publisher : Springer
Page : 153 pages
File Size : 33,51 MB
Release : 2003-07-01
Category : Mathematics
ISBN : 3540452761

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- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of approach dynamical systems generated by equations, etc., properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study).