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The Numerical Solution Of A Nonlinear Wave Equation From Solid State Physics
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Book Synopsis Nonlinear Waves in Solid State Physics by : A.D. Boardman
Download or read book Nonlinear Waves in Solid State Physics written by A.D. Boardman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the contributions to the 17th International School of Materials Sci ence and Technology, entitled Nonlinear Waves in Solid State Physics. This was held as a NATO Advanced Study Institute at the Ettore Majorana Centre in Erice, Sicily between the st th 1 and 15 July 1989, and attracted almost 100 participants from over 20 different countries. The book covers the fundamental properties of nonlinear waves in solid state materials, dealing with both theory and experiment. The aim is to emphasise the methods underpinning the important new developments in this area. The material is organised into subject areas that can broadly be classified into the following groups: the theory of nonlinear surface and guided waves in self-focusing magnetic and non-magnetic materials; nonlinear effects at in terfaces; nonlinear acoustoelectronic and surface acoustic waves; Lagrangian and Hamiltonian formulations of nonlinear problems; nonlinear effects in optical fibres; resonance phenomena; and nonlinear integrated optics. The chapters have been grouped together according to these classifications as closely as possible, but it should be borne in mind that although there is much overlap of ideas, each chapter is essentially independent of the others. We would like to acknowledge the sponsorship of the NATO Scientific Affairs Division, the European Physical Society, the National Science Foundation of the USA, the European Research Office, the Italian Ministry of Education, the Italian Ministry of Scientific and Technological Research, the Sicilian Regional Government and the Ugo Bordoni Foundation.
Book Synopsis Intelligent Mathematics II: Applied Mathematics and Approximation Theory by : George A. Anastassiou
Download or read book Intelligent Mathematics II: Applied Mathematics and Approximation Theory written by George A. Anastassiou and published by Springer. This book was released on 2016-03-21 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.
Book Synopsis The Optimal Homotopy Asymptotic Method by : Vasile Marinca
Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Book Synopsis Nonlinear Optical Waves by : A.I. Maimistov
Download or read book Nonlinear Optical Waves written by A.I. Maimistov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: A non-linear wave is one of the fundamental objects of nature. They are inherent to aerodynamics and hydrodynamics, solid state physics and plasma physics, optics and field theory, chemistry reaction kinetics and population dynamics, nuclear physics and gravity. All non-linear waves can be divided into two parts: dispersive waves and dissipative ones. The history of investigation of these waves has been lasting about two centuries. In 1834 J. S. Russell discovered the extraordinary type of waves without the dispersive broadening. In 1965 N. J. Zabusky and M. D. Kruskal found that the Korteweg-de Vries equation has solutions of the solitary wave form. This solitary wave demonstrates the particle-like properties, i. e. , stability under propagation and the elastic interaction under collision of the solitary waves. These waves were named solitons. In succeeding years there has been a great deal of progress in understanding of soliton nature. Now solitons have become the primary components in many important problems of nonlinear wave dynamics. It should be noted that non-linear optics is the field, where all soliton features are exhibited to a great extent. This book had been designed as the tutorial to the theory of non-linear waves in optics. The first version was projected as the book covering all the problems in this field, both analytical and numerical methods, and results as well. However, it became evident in the process of work that this was not a real task.
Book Synopsis Proceedings of the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024), Volume 1 by : Asit Saha
Download or read book Proceedings of the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024), Volume 1 written by Asit Saha and published by Springer Nature. This book was released on with total page 709 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Integrators for Differential Equations with Highly Oscillatory Solutions by : Xinyuan Wu
Download or read book Geometric Integrators for Differential Equations with Highly Oscillatory Solutions written by Xinyuan Wu and published by Springer Nature. This book was released on 2021-09-28 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations. Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions.
Book Synopsis Advanced Numerical Methods for Differential Equations by : Harendra Singh
Download or read book Advanced Numerical Methods for Differential Equations written by Harendra Singh and published by CRC Press. This book was released on 2021-06-25 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.
Book Synopsis Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations by : Geeta Arora
Download or read book Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations written by Geeta Arora and published by CRC Press. This book was released on 2024-01-23 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems. The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.
Book Synopsis Partial Differential Equations and Solitary Waves Theory by : Abdul-Majid Wazwaz
Download or read book Partial Differential Equations and Solitary Waves Theory written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.
Book Synopsis Nonlinear Differential Equations in Physics by : Santanu Saha Ray
Download or read book Nonlinear Differential Equations in Physics written by Santanu Saha Ray and published by Springer Nature. This book was released on 2019-12-28 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses various novel analytical and numerical methods for solving partial and fractional differential equations. Moreover, it presents selected numerical methods for solving stochastic point kinetic equations in nuclear reactor dynamics by using Euler–Maruyama and strong-order Taylor numerical methods. The book also shows how to arrive at new, exact solutions to various fractional differential equations, such as the time-fractional Burgers–Hopf equation, the (3+1)-dimensional time-fractional Khokhlov–Zabolotskaya–Kuznetsov equation, (3+1)-dimensional time-fractional KdV–Khokhlov–Zabolotskaya–Kuznetsov equation, fractional (2+1)-dimensional Davey–Stewartson equation, and integrable Davey–Stewartson-type equation. Many of the methods discussed are analytical–numerical, namely the modified decomposition method, a new two-step Adomian decomposition method, new approach to the Adomian decomposition method, modified homotopy analysis method with Fourier transform, modified fractional reduced differential transform method (MFRDTM), coupled fractional reduced differential transform method (CFRDTM), optimal homotopy asymptotic method, first integral method, and a solution procedure based on Haar wavelets and the operational matrices with function approximation. The book proposes for the first time a generalized order operational matrix of Haar wavelets, as well as new techniques (MFRDTM and CFRDTM) for solving fractional differential equations. Numerical methods used to solve stochastic point kinetic equations, like the Wiener process, Euler–Maruyama, and order 1.5 strong Taylor methods, are also discussed.
Book Synopsis Handbook of Fractional Calculus for Engineering and Science by : Harendra Singh
Download or read book Handbook of Fractional Calculus for Engineering and Science written by Harendra Singh and published by CRC Press. This book was released on 2022-02-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1989 with total page 1398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1976 with total page 1288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Technical Abstract Bulletin written by and published by . This book was released on 1967 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Waves, Solitons and Chaos by : Eryk Infeld
Download or read book Nonlinear Waves, Solitons and Chaos written by Eryk Infeld and published by Cambridge University Press. This book was released on 2000-07-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of a highly successful book on nonlinear waves, solitons and chaos.
Book Synopsis Non-Equilibrium Dynamics of Semiconductors and Nanostructures by : Kong-Thon Tsen
Download or read book Non-Equilibrium Dynamics of Semiconductors and Nanostructures written by Kong-Thon Tsen and published by CRC Press. This book was released on 2018-10-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of the femto-second laser has enabled us to observe phenomena at the atomic timescale. One area to reap enormous benefits from this ability is ultrafast dynamics. Collecting the works of leading experts from around the globe, Non-Equilibrium Dynamics of Semiconductors and Nanostructures surveys recent developments in a variety of areas in ultrafast dynamics. In eight authoritative chapters illustrated by more than 150 figures, this book spans a broad range of new techniques and advances. It begins with a review of spin dynamics in a high-mobility two-dimensional electron gas, followed by the generation, propagation, and nonlinear properties of high-amplitude, ultrashort strain solitons in solids. The discussion then turns to nonlinear optical properties of nanoscale artificial dielectrics, optical properties of GaN self-assembled quantum dots, and optical studies of carrier dynamics and non-equilibrium optical phonons in nitride-based semiconductors. Rounding out the presentation, the book examines ultrafast non-equilibrium electron dynamics in metal nanoparticles, monochromatic acoustic phonons in GaAs, and electromagnetically induced transparency in semiconductor quantum wells. With its pedagogical approach and practical, up-to-date coverage, Non-Equilibrium Dynamics of Semiconductors and Nanostructures allows you to easily put the material into practice, whether you are a seasoned researcher or new to the field.
