New Numerical And Analytical Methods For Nonlinear Partial Differential Equations With Applications In Quantum Physics

Author : Mustafa Inc
Publisher : Frontiers Media SA
ISBN 13 : 2832539432
Total Pages : 160 pages
Book Rating : 4.39/5 ( download)

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Download or read book New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics written by Mustafa Inc and published by Frontiers Media SA. This book was released on 2023-11-20 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws

Author : Jesus Martin-Vaquero
Publisher : Frontiers Media SA
ISBN 13 : 2889714241
Total Pages : 96 pages
Book Rating : 4.47/5 ( download)

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Download or read book Analytical and Numerical Methods for Differential Equations and Applications written by Jesus Martin-Vaquero and published by Frontiers Media SA. This book was released on 2021-10-29 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : P.A. Clarkson
Publisher : Springer Science & Business Media
ISBN 13 : 940112082X
Total Pages : 466 pages
Book Rating : 4.21/5 ( download)

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Download or read book Applications of Analytic and Geometric Methods to Nonlinear Differential Equations written by P.A. Clarkson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.

Author : Roland Glowinski
Publisher : Springer Science & Business Media
ISBN 13 : 1402087586
Total Pages : 294 pages
Book Rating : 4.85/5 ( download)

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Download or read book Partial Differential Equations written by Roland Glowinski and published by Springer Science & Business Media. This book was released on 2008-06-26 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.

Author : Bruno Carpentieri
Publisher : BoD – Books on Demand
ISBN 13 : 1839686561
Total Pages : 374 pages
Book Rating : 4.66/5 ( download)

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Download or read book Recent Developments in the Solution of Nonlinear Differential Equations written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-09-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Author : Michael Hintermüller
Publisher : Springer Nature
ISBN 13 : 3030331164
Total Pages : 396 pages
Book Rating : 4.60/5 ( download)

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Download or read book Topics in Applied Analysis and Optimisation written by Michael Hintermüller and published by Springer Nature. This book was released on 2019-11-27 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
ISBN 13 : 0817644180
Total Pages : 738 pages
Book Rating : 4.85/5 ( download)

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Download or read book Nonlinear Partial Differential Equations for Scientists and Engineers written by Lokenath Debnath and published by Springer Science & Business Media. This book was released on 2010-02-20 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded, revised edition is a thorough and systematic treatment of linear and nonlinear partial differential equations and their varied applications. It contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, make the book useful for a diverse readership including graduates, researchers, and professionals in mathematics, physics and engineering.

Author : Hristos T. Anastassiu
Publisher : MDPI
ISBN 13 : 3036500642
Total Pages : 196 pages
Book Rating : 4.45/5 ( download)

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Download or read book Numerical and Analytical Methods in Electromagnetics written by Hristos T. Anastassiu and published by MDPI. This book was released on 2021-03-19 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like all branches of physics and engineering, electromagnetics relies on mathematical methods for modeling, simulation, and design procedures in all of its aspects (radiation, propagation, scattering, imaging, etc.). Originally, rigorous analytical techniques were the only machinery available to produce any useful results. In the 1960s and 1970s, emphasis was placed on asymptotic techniques, which produced approximations of the fields for very high frequencies when closed-form solutions were not feasible. Later, when computers demonstrated explosive progress, numerical techniques were utilized to develop approximate results of controllable accuracy for arbitrary geometries. In this Special Issue, the most recent advances in the aforementioned approaches are presented to illustrate the state-of-the-art mathematical techniques in electromagnetics.

Author : Attilio Maccari
Publisher : John Wiley & Sons
ISBN 13 : 3527414215
Total Pages : 261 pages
Book Rating : 4.15/5 ( download)

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Download or read book Asymptotic Perturbation Methods written by Attilio Maccari and published by John Wiley & Sons. This book was released on 2023-04-10 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohesive overview of powerful mathematical methods to solve differential equations in physics Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method. Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphasis on applications. There are several examples included throughout the text, and, crucially, the scientific background is explained at an elementary level and closely integrated with the mathematical theory to enable seamless reader comprehension. To fully understand the concepts within this book, the prerequisites are multivariable calculus and introductory physics. Written by a highly qualified author with significant accomplishments in the field, Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics covers sample topics such as: Application of the various flavors of the asymptotic perturbation method, such as the Maccari method to the governing equations of nonlinear system Nonlinear oscillators, limit cycles, and their bifurcations, iterated nonlinear maps, continuous systems, and nonlinear partial differential equations (NPDEs) Nonlinear systems, such as the van der Pol oscillator, with advanced coverage of plasma physics, quantum mechanics, elementary particle physics, cosmology, and chaotic systems Infinite-period bifurcation in the nonlinear Schrodinger equation and fractal and chaotic solutions in NPDEs Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics is ideal for an introductory course at the senior or first year graduate level. It is also a highly valuable reference for any professional scientist who does not possess deep knowledge about nonlinear physics.

Author : B. N. Chetverushkin
Publisher : Springer
ISBN 13 : 3319783254
Total Pages : 452 pages
Book Rating : 4.53/5 ( download)

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Download or read book Contributions to Partial Differential Equations and Applications written by B. N. Chetverushkin and published by Springer. This book was released on 2018-07-19 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats Modelling of CFD problems, Numerical tools for PDE, and Scientific Computing and Systems of ODE for Epidemiology, topics that are closely related to the scientific activities and interests of Prof. William Fitzgibbon, Prof. Yuri Kuznetsov, and Prof. O. Pironneau, whose outstanding achievements are recognised in this volume. It contains 20 contributions from leading scientists in applied mathematics dealing with partial differential equations and their applications to engineering, ab-initio chemistry and life sciences. It includes the mathematical and numerical contributions to PDE for applications presented at the ECCOMAS thematic conference "Contributions to PDE for Applications" held at Laboratoire Jacques Louis Lions in Paris, France, August 31- September 1, 2015, and at the Department of Mathematics, University of Houston, Texas, USA, February 26-27, 2016. This event brought together specialists from universities and research institutions who are developing or applying numerical PDE or ODE methods with an emphasis on industrial and societal applications. This volume is of interest to researchers and practitioners as well as advanced students or engineers in applied and computational mathematics. All contributions are written at an advanced scientific level with no effort made by the editors to make this volume self-contained. It is assumed that the reader is a specialist already who knows the basis of this field of research and has the capability of understanding and appreciating the latest developments in this field.