HANDBOOK OF EXACT SOLUTIONS TO THE NONLINEAR SCHROEDINGER EQUATIONS, SECOND EDITION.
Author: USAMA. AL SAKKAF AL KHAWAJA (LAILA.)
Publisher:
Published: 2024
Total Pages: 0
ISBN-13: 9780750359528
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Handbook of Exact Solutions to the Nonlinear Schrödinger Equations
Author: Usama Al Khawaja
Publisher:
Published: 2019
Total Pages: 0
ISBN-13: 9780750324281
DOWNLOAD EBOOK →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
Author: Andrei D. Polyanin
Publisher: CRC Press
Published: 2004-06-02
Total Pages: 835
ISBN-13: 1135440816
DOWNLOAD EBOOK →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 the Nonlinear Schrödinger Equations
Author: Usama Al Khawaja
Publisher:
Published: 2019
Total Pages:
ISBN-13: 9780750324274
DOWNLOAD EBOOK →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, Second Edition
Author: Andrei D. Polyanin
Publisher: Chapman and Hall/CRC
Published: 2011-12-16
Total Pages: 0
ISBN-13: 9781420087239
DOWNLOAD EBOOK →New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.
Handbook of Exact Solutions for Ordinary Differential Equations
Author: Valentin F. Zaitsev
Publisher: CRC Press
Published: 2002-10-28
Total Pages: 815
ISBN-13: 1420035339
DOWNLOAD EBOOK →Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handboo
Handbook of Ordinary Differential Equations
Author: Andrei D. Polyanin
Publisher: CRC Press
Published: 2017-11-15
Total Pages: 1767
ISBN-13: 1351643916
DOWNLOAD EBOOK →The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics
Author: Victor A. Galaktionov
Publisher: CRC Press
Published: 2006-11-02
Total Pages: 530
ISBN-13: 1420011626
DOWNLOAD EBOOK →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
Handbook of Integral Equations
Author: Andrei D. Polyanin
Publisher: CRC Press
Published: 2008-02-12
Total Pages: 1143
ISBN-13: 0203881052
DOWNLOAD EBOOK →Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
Handbook of Exact Solutions to Mathematical Equations
Author: Andrei D. Polyanin
Publisher: CRC Press
Published: 2024-08-14
Total Pages: 0
ISBN-13: 9780367507992
DOWNLOAD EBOOK →"This Handbook is a unique reference for scientists and engineers, containing over 3,800 nonlinear partial differential equations with solutions. The book concerns first-, second-, third-, fourth-, and higher-order nonlinear PDEs and systems of coupled PDEs. It discusses parabolic, hyperbolic, and elliptic equations as well as those of mixed and general type. All in all, the handbook contains many more nonlinear equations of mathematical physics and other nonlinear PDEs with their exact solutions, than any other book currently available. Apart from the exact solutions, it also provides various reductions and transformations leading to ordinary differential equations, linear PDEs, or simpler PDEs. A solution is called exact if, when substituted into the differential equation under consideration, it turns the equation into an identity. In this case, no approximations or simplifications of the equation are allowed, and no a priori assumptions are used. Exact solutions to nonlinear equations of mathematical physics are understood as follows: solutions expressed in terms of elementary functions, functions included in the equation (this is necessary when the equation depends on arbitrary functions), and indefinite integrals; solutions expressed in terms of solutions to ordinary differential equations or systems of such equations. Exact solutions of mathematical equations have always played and continue to play a massive role in forming a correct understanding of the qualitative features of many phenomena and processes in various fields of natural science. The book will be helpful for a wide range of researchers, university teachers, and graduate and postgraduate students specializing in the fields of applied and computational mathematics, mathematical and theoretical physics, continuum mechanics, control theory, biology, biophysics, biochemistry, medicine, chemical engineering sciences, and ecology"--
