Download or read book Solitons in Two Dimensional Shallow Water written by Yuji Kodama and published by SIAM. This book was released on 2018-12-10 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools?algebraic geometry, algebraic combinatorics, and representation theory, among others?are used to analyze these two-dimensional wave patterns. The author?s primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.
Download or read book Nonlinear Dispersive Equations written by Christian Klein and published by Springer Nature. This book was released on 2021 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Download or read book Geometric Mechanics and Its Applications written by Weipeng Hu and published by Springer Nature. This book was released on 2023-01-01 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: To make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.
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.
Download or read book Nonlinear and Modern Mathematical Physics written by Solomon Manukure and published by Springer Nature. This book was released on with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Conference on Water Waves Theory and Experiment Howard University USA 13 18 May 2008 written by M. F. Mahmood and published by World Scientific. This book was released on 2010 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to introduce new researchers to the rich dynamical system of water waves, and to show how (some) abstract mathematical concepts can be applied fruitfully in a practical physical problem and to make the connection between theory and experiment. It provides a coherent set of lectures on the current status of water wave theory, including identification of some open problems.
Download or read book Nonlinear Physics of Plasmas written by Mitsuo Kono and published by Springer Science & Business Media. This book was released on 2010-10-17 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.
Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Download or read book Rogue Waves in the Ocean written by Christian Kharif and published by Springer Science & Business Media. This book was released on 2008-12-11 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: “It came from nowhere, snapping giant ships in two. No one believed the survivors . . . until now” —New Scientist magazine cover, June 30, 2001 Rogue waves are the focus of this book. They are among the waves naturally - served by people on the sea surface that represent an inseparable feature of the Ocean. Rogue waves appear from nowhere, cause danger, and disappear at once. They may occur on the surface of a relatively calm sea and not reach very high amplitudes, but still be fatal for ships and crew due to their unexpectedness and abnormal features. Seamen are known to be unsurpassed authors of exciting and horrifying stories about the sea and sea waves. This could explain why, despite the increasing number of documented cases, that sailors’ observations of “walls of - ter” have been considered ctitious for a while. These stories are now addressed again due to the amount of doubtless evidence of the existence of the phenomenon, but still without suf cient information to - able interested researchers and engineers to completely understand it. The billows appear suddenly, exceeding the surrounding waves by two times their size and more, and obtaining many names: abnormal, exceptional, extreme, giant, huge, s- den, episodic, freak, monster, rogue, vicious, killer, mad- or rabid-dog waves, cape rollers, holes in the sea, walls of water, three sisters, etc.
Download or read book Rossby Vortices Spiral Structures Solitons written by Mikhail V. Nezlin and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book can be looked upon in more ways than one. On the one hand, it describes strikingly interesting and lucid hydrodynamic experiments done in the style of the "good old days" when the physicist needed little more than a piece of string and some sealing wax. On the other hand, it demonstrates how a profound physical analogy can help to get a synoptic view on a broad range of nonlinear phenomena involving self-organization of vortical structures in planetary atmo spheres and oceans, in galaxies and in plasmas. In particular, this approach has elucidated the nature and the mechanism of such grand phenomena as the Great of galaxies. A number of our Red Spot vortex on Jupiter and the spiral arms predictions concerning the dynamics of spiral galaxies are now being confirmed by astronomical observations stimulated by our experiments. This book is based on the material most of which was accumulated during 1981-88 in close cooperation with our colleagues, experimenters from the Plasma Physics Department of the Kurchatov Atomic Energy Institute (S. V. Antipov, A. S. Trubnikov, AYu. Rylov, AV. Khutoretsky) and astrophysics theoreticians from the Astronomical Council of the USSR Academy of Sciences (AM. Frid man) and from the Volgograd State University (AG. Morozov). To all of them we wish to express our gratitude. Whenever we speak of "our experiments", the participation of the entire team is implied.
Download or read book Solitons written by Mohamed Atef Helal and published by Springer Nature. This book was released on 2022-11-12 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This newly updated volume of the Encyclopedia of Complexity and Systems Science (ECSS) presents several mathematical models that describe this physical phenomenon, including the famous non-linear equation Korteweg-de-Vries (KdV) that represents the canonical form of solitons. Also, there exists a class of nonlinear partial differential equations that led to solitons, e.g., Kadomtsev-Petviashvili (KP), Klein-Gordon (KG), Sine-Gordon (SG), Non-Linear Schrödinger (NLS), Korteweg-de-Vries Burger’s (KdVB), etc. Different linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Other non-analytic methods use the computational techniques available in such popular mathematical packages as Mathematica, Maple, and MATLAB. The main purpose of this volume is to provide physicists, engineers, and their students with the proper methods and tools to solve the soliton equations, and to discover the new possibilities of using solitons in multi-disciplinary areas ranging from telecommunications to biology, cosmology, and oceanographic studies.
Download or read book Waves Called Solitons written by Michel Remoissenet and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encouraged by the friendly reception given to the first edition, I have preserved its basic form and most of the details. Apart from some corrections, minor changes, and addition of references where it was necessary, I have made the following changes. Chapter 1 was expanded by a discussion of the discovery of soli tons in the field of electromagnetic waves and optics. A new section devoted to nonlinear transmission lines and their applications in the microwave range has been added to Chap. 3. It seems to me that it was important to describe laboratory experiments on modulational instability, and subsequent generation of solitons, both in electrical transmission lines and in deep water in Chaps. 4 and 5. A description of a very simple experimental pocket version of the mechanical transmission line has been included in Chap. 6. Such a versatile and useful device should stimulate a practical approach to soli ton physics. Chapter 7 was completed by a short presentation of some recent experimental results on discrete Josephson transmission lines. A discussion of the experimental modulational instability of coupled optical waves and a simple look at quantum solitons were added to Chap. 8 in order to introduce the reader to such remarkable topics. Of the many people who made valuable comments on the first edition, I am particularly grateful to M. Dragoman, Y. S. Kivshar and A. W. Snyder. I would like to thank R. S. MacKay whose corrections and suggestions helped refine the manuscript of this second edition.
Download or read book The Direct Method in Soliton Theory written by Ryogo Hirota and published by Cambridge University Press. This book was released on 2004-07-22 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Account of method of solving soliton equations by the inventor of the method.
Download or read book Solitons in Mathematics and Physics written by Alan C. Newell and published by SIAM. This book was released on 1985-06-01 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.
Download or read book Solitons and the Inverse Scattering Transform written by Mark J. Ablowitz and published by SIAM. This book was released on 2006-05-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.
Download or read book Solitons In Multidimensions Inverse Spectral Transform Method written by B G Konopelchenko and published by World Scientific. This book was released on 1993-04-30 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations.
