Author: Dae-il Choi
Publisher:
ISBN:
Category : Schrödinger equation
Languages : en
Pages : 324

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Book Description

Author: Luis Vazquez
Publisher: World Scientific
ISBN: 981454809X
Category :
Languages : en
Pages : 382

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Book Description
This is the first of two Euroconferences aimed at addressing the issues of Nonlinearity and Disorder. The 1995 Euroconference was devoted to the mathematical, numerical and experimental studies related to the Klein-Gordon and Schrödinger systems. The Euroconference was organized around main lectures in each area to introduce the main concepts and stimulate discussions. The mathematical studies covered the functional anlaysis and stochastic techniques applied to the general Klein-Gordon and Schrödinger wave equations. Also a panoramic view of the numerical schemes was presented to simulate the above equations, as well as an overview of the applications of such systems in the areas of condensed matter, optical physics, new materials and biophysics. Special attention was devoted to the discrete Schrödinger and Klein-Gordon systems and their applications.

Author: Mark J. Ablowitz
Publisher: World Scientific
ISBN: 9812382704
Category : Science
Languages : en
Pages : 438

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Book Description
The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems ? both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).

Author: B. M. Herbst
Publisher: Longman Sc & Tech
ISBN: 9780582014817
Category : Schrödinger equation
Languages : en
Pages : 208

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Book Description

Author: Luis Vázquez
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789810225650
Category : Science
Languages : en
Pages : 363

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Book Description

Author: Barbara Prinari
Publisher: World Scientific
ISBN: 9814486698
Category : Science
Languages : en
Pages : 438

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Book Description
The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems — both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).

Author: Elena Tobisch
Publisher: Springer
ISBN: 3319206907
Category : Science
Languages : en
Pages : 309

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Book Description
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g. equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima, KdV-type, Klein-Gordon, NLS-type, Serre, Shamel , Whitham and Zakharov. This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics.

Author: Amelia Bucur
Publisher: Cambridge Scholars Publishing
ISBN: 1527593843
Category : Mathematics
Languages : en
Pages : 247

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Book Description
This scientific book was written for specialists on the theory and application of numerical approximation techniques, primarily for mathematicians, scientists, and engineers. The book outlines numerical methods and their applications for systems of linear and nonlinear equations, interpolation, numerical integration and solving problems with differential equations, partial differential equations or fractional differential equations. It explores techniques in C++, Maple, and MATLAB, develops mathematical methods through computation and develops numerical methods in the context of case studies for data analysis, optimisation, linear algebra and differential equations.

Author: M. J. Ablowitz
Publisher: Cambridge University Press
ISBN: 9780521534376
Category : Mathematics
Languages : en
Pages : 276

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Book Description
This book presents a detailed mathematical analysis of scattering theory, obtains soliton solutions, and analyzes soliton interactions, both scalar and vector.

Author: Xinyuan Wu
Publisher: Springer
ISBN: 9811090041
Category : Mathematics
Languages : en
Pages : 356

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Book Description
The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.