Handbook Of Exact Solutions To The Nonlinear Schr Dinger Equations
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Handbook Of Exact Solutions To The Nonlinear Schr Dinger Equations
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Author : Usama Al Khawaja
language : en
Publisher: Institute of Physics Publishing
Release Date : 2019-11-15
Handbook Of Exact Solutions To The Nonlinear Schr Dinger Equations written by Usama Al Khawaja and has been published by Institute of Physics Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-15 with Science categories.
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.
Handbook Of Exact Solutions To The Nonlinear Schr Dinger Equations Second Edition
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Author : Usama Al Khawaja
language : en
Publisher:
Release Date : 2024-06-28
Handbook Of Exact Solutions To The Nonlinear Schr Dinger Equations Second Edition written by Usama Al Khawaja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-28 with Science categories.
Handbook Of Exact Solutions To The Nonlinear Schr Dinger Equations
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Author : Usama Al Khawaja
language : en
Publisher:
Release Date : 2019
Handbook Of Exact Solutions To The Nonlinear Schr Dinger Equations written by Usama Al Khawaja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with SCIENCE categories.
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.
Handbook Of Nonlinear Partial Differential Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2004-06-02
Handbook Of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-02 with Mathematics categories.
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, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Handbook Of Exact Solutions To Mathematical Equations
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Author : A. D. Polianin
language : en
Publisher:
Release Date : 2024-07
Handbook Of Exact Solutions To Mathematical Equations written by A. D. Polianin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07 with Mathematics categories.
Handbook Of Exact Solutions To Mathematical Equations
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Author : Andrei D. Polyanin
language : en
Publisher: CRC Press
Release Date : 2024-08-26
Handbook Of Exact Solutions To Mathematical Equations written by Andrei D. Polyanin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-26 with Mathematics categories.
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.
Exact Solutions For A Generalized Nonlinear Schr Dinger Equation
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Author : Morris, J. Ll. (John Ll.)
language : en
Publisher: University of Waterloo, Faculty of Mathematics
Release Date : 1988
Exact Solutions For A Generalized Nonlinear Schr Dinger Equation written by Morris, J. Ll. (John Ll.) and has been published by University of Waterloo, Faculty of Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Differential equations, Nonlinear categories.
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."
Global Solutions Of Nonlinear Schrodinger Equations
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Author : Jean Bourgain
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Global Solutions Of Nonlinear Schrodinger Equations written by Jean Bourgain and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This volume presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with Large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented and several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example, the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.
Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics
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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2006-11-02
Exact Solutions And Invariant Subspaces Of Nonlinear Partial Differential Equations In Mechanics And Physics written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-02 with Mathematics categories.
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 focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties. This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Exact Solutions Of Multidimensional Nonlinear Dirac S And Schr Dinger S Equations
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Author : W. I. Fushchich
language : en
Publisher:
Release Date : 1988
Exact Solutions Of Multidimensional Nonlinear Dirac S And Schr Dinger S Equations written by W. I. Fushchich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.