Introduction to Pdes and Waves for the Atmosphere and Ocean (Courant Lecture Notes)

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Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, where rigorous mathematical analysis as well as asymptotic, qualitative, and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics, although a serious reader should supplement these notes with material such as additional information on geophysical flows, as suggested in the preface.

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The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts. Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts in gas dynamics, a graphical presentation of the results of extensive numerical computations, and an extension of Fermat's principle. There is also a chapter containing approximate equations used to discuss stability of steady transonic flows. Full of new and original results, Nonlinear Hyperbolic Waves in Multidimensions is your only opportunity to explore a full treatment of these recent findings in book form. The material presented in this volume will prove useful not only for solving practical problems, but also in raising many difficult but important mathematical questions that remain open.

Discrete and Continuous Nonlinear Schrödinger Systems (London Mathematical Society Lecture Note Series)

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Discrete and Continuous Nonlinear Schrödinger Systems (London Mathematical Society Lecture Note Series)
M. J. Ablowitz , B. Prinari , and A. D. Trubatch
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521534372

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Over the past thirty years significant progress has been made in the investigation of nonlinear waves--including "soliton equations", a class of nonlinear wave equations that arise frequently in such areas as nonlinear optics, fluid dynamics, and statistical physics. The broad interest in this field can be traced to understanding "solitons" and the associated development of a method of solution termed the inverse scattering transform (IST). The IST technique applies to continuous and discrete nonlinear Schrödinger (NLS) equations of scalar and vector type. This work presents a detailed mathematical study of the scattering theory, offers soliton solutions, and analyzes both scalar and vector soliton interactions. The authors provide advanced students and researchers with a thorough and self-contained presentation of the IST as applied to nonlinear Schrödinger systems.

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In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schr_dinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature.

Nonlinear Wave Equations Perturbed by Viscous Terms (De Gruyter Expositions in Mathematics, 31)

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Nonlinear Wave Equations Perturbed by Viscous Terms (De Gruyter Expositions in Mathematics, 31)
V. P. Maslov , and Petr Petrovich Mosolov
Manufacturer: Walter de Gruyter
ProductGroup: Book
Binding: Hardcover

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Lectures on Nonlinear Wave Equations (Monographs in Analysis)

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Lectures on Nonlinear Wave Equations (Monographs in Analysis)
Christopher D. Sogge
Manufacturer: Intl Pr
ProductGroup: Book
Binding: Hardcover

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ASIN: 1571460322
Release Date: 1995-08-01

Solitons in Field Theory and Nonlinear Analysis (Springer Monographs in Mathematics)

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Solitons in Field Theory and Nonlinear Analysis (Springer Monographs in Mathematics)
Yisong Yang
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 038795242X

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This book is on soliton solutions of elliptical partial differential equations arising in quantum field theory, such as vortices, instantons, monopoles, dyons, and cosmic strings. The book presents in-depth description of the problems of current interest, forging a link between mathematical analysis and physics and seeking to stimulate further research in the area. Physically, it touches the major branches of field theory: classical mechanics, special relativity, Maxwell equations, superconductivity, Yang-Mills gauge theory, general relativity, and cosmology. Mathematically, it involves Riemannian geometry, Lie groups and Lie algebras, algebraic topology (characteristic classes and homotropy) and emphasizes modern nonlinear functional analysis. There are many interesting and challenging problems in the area of classical field theory, and while this area has long been of interest to algebraists, geometers, and topologists, it has gradually begun to attract the attention of more analysts. This book written for researchers and graduate students will appeal to high-energy and condensed-matter physicists, mathematicians, and mathematical scientists.

Travelling Waves in Nonlinear Diffusion-Convection Reaction (Progress in Nonlinear Differential Equations and Their Applications)

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Travelling Waves in Nonlinear Diffusion-Convection Reaction (Progress in Nonlinear Differential Equations and Their Applications)
Brian H. Gilding , and Robert Kersner
Manufacturer: Birkhäuser Basel
ProductGroup: Book
Binding: Hardcover

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ASIN: 3764370718

Book Description

Travelling waves are observed in many natural processes, ranging from the spread of diseases to the combustion of fuels. The book is concerned with characterizing such waves in phenomena described by a nonlinear diffusion-convection-reaction equation. The technique employed is new and can be briefly described as an integral or integrated approach to phase-plane analysis. It leads to results which were so far unobtainable, including the effects of degenerate diffusion and nonlinear convection, or are much sharper than those obtained previously. Applications are taken from the evolution of biological populations, diffusion of oxygen in tissue, heat transfer, thermal convection, combustion, flow in porous media, hydrology, soil-moisture flow, boundary layer theory, foam drainage, viscous fluid flow, turbulent fluid flow, the motion of plasma particles in a magnetic field, solar prominences, crystal growth, reaction chemistry, quenching, and other fields.

In this way, the book brings together and improves a large number of results which have been obtained piecemeal in many different scientific disciplines. It provides a reference work for applications of nonlinear diffusion, convection and reaction, and gives a state-of-the-art survey of the study of the occurrence of travelling waves in such applications.

Local And Global Analysis of Nonlinear Dispersive And Wave Equations (Cbms Regional Conference Series in Mathematics) (Cbms Regional Conference Series in Mathematics)

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Local And Global Analysis of Nonlinear Dispersive And Wave Equations (Cbms Regional Conference Series in Mathematics) (Cbms Regional Conference Series in Mathematics)
Terence Tao
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

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ASIN: 0821841432

Product Description

Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations. Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems. As the subject is vast, the book does not attempt to give a comprehensive survey of the field, but instead concentrates on a representative sample of results for a selected set of equations, ranging from the fundamental local and global existence theorems to very recent results, particularly focusing on the recent progress in understanding the evolution of energy-critical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE. Readership Graduate students and research mathematicians interested in nonlinear partial differential equations.

Nonlinear Wave Dynamics: Complexity and Simplicity (Texts in the Mathematical Sciences)

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Nonlinear Wave Dynamics: Complexity and Simplicity (Texts in the Mathematical Sciences)
J. Engelbrecht
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Book Description

The general idea advocated in this book is to start from complicated mathematical models describing wave motion as it results from the rules of continuum mechanics and then to find a simpler viewpoint that still keeps everything essential preserved. Special attention is paid to the description of the sources of nonlinearities. The complexities in modelling are demonstrated by several examples including solitons, propagating instabilities and waves in waveguides. The selected case studies show some unconventional approaches in order to explain the richness of nonlinear wave motion. The final chapters are of more general character, including the essays on nonlinearity, beauty, and complexity. In this way, the thread of the analysis is the following: simple basic arguments result in a complicated theory that, in turn, needs certain simplifications in order to grasp the physical phenomena involved. What makes this book special compared to other books in the field is that all the examples are cast into a general philosophical network of complexity and simplicity.
Audience: This volume will be of interest to researchers and students whose work involves mathematical modelling of wave phenomena.

Nonlinear Wave Equations (Cbms Regional Conference Series in Mathematics)

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Nonlinear Wave Equations (Cbms Regional Conference Series in Mathematics)
Walter A. Strauss
Manufacturer: Amer Mathematical Society
ProductGroup: Book
Binding: Paperback

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ASIN: 0821807250

Book Description

The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves.

This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area. The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrödinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations.

The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.

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For lovers of timeless classics, this series of beautifully packaged and affordably priced editions of world literature encompasses a variety of literary genres, including theater, novels, poems, and essays.

Los lectores tomarán un gran placer en descubrir los clásicos con estas bellas y económicas ediciones de literatura famosa y universal. Esta selección editorial cuenta con títulos que abarcan todos los géneros literarios, desde teatro, narrativa, poesía y el ensayo.

Día de campo: Fernando de Ita: Día de campo no es una obra complaciente en ningún sentido; exige del espectador todo su intelecto y toda su sensibilidad, ... de teatro): An article from: Siempre!

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Día de campo: Fernando de Ita: Día de campo no es una obra complaciente en ningún sentido; exige del espectador todo su intelecto y toda su sensibilidad, ... de teatro): An article from: Siempre!
Gonzalo Valdés Medellín
Manufacturer: Thomson Gale
ProductGroup: Book
Binding: Digital
ASIN: B0008264VO
Release Date: 2006-10-24

Book Description

This digital document is an article from Siempre!, published by Thomson Gale on February 15, 2004. The length of the article is 710 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

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Title: Día de campo: Fernando de Ita: Día de campo no es una obra complaciente en ningún sentido; exige del espectador todo su intelecto y toda su sensibilidad, despojados de todo prejuicio; toda su honestidad.(Reseña de teatro)
Author: Gonzalo Valdés Medellín
Publication: Siempre! (Magazine/Journal)
Date: February 15, 2004
Publisher: Thomson Gale
Volume: 50 Issue: 2644 Page: 69(1)

Article Type: Reseña de teatro

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Sentido (del humor) y sensibilidad.(Greta Mulrooney, escritora Británica)(TT: Sense of humor and sensitivity.)(TA: Gretta Mulrooney, British writer)(Reseña): An article from: Epoca

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Sentido (del humor) y sensibilidad.(Greta Mulrooney, escritora Británica)(TT: Sense of humor and sensitivity.)(TA: Gretta Mulrooney, British writer)(Reseña): An article from: Epoca
Angel Vivas
Manufacturer: Difusora de Informacion Periodica, S.A. (DINPESA)
ProductGroup: Book
Binding: Digital
ASIN: B00099LRAE
Release Date: 2005-07-28

Book Description

This digital document is an article from Epoca, published by Difusora de Informacion Periodica, S.A. (DINPESA) on December 20, 1999. The length of the article is 769 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Sentido (del humor) y sensibilidad.(Greta Mulrooney, escritora Británica)(TT: Sense of humor and sensitivity.)(TA: Gretta Mulrooney, British writer)(Reseña)
Author: Angel Vivas
Publication: Epoca (Magazine/Journal)
Date: December 20, 1999
Publisher: Difusora de Informacion Periodica, S.A. (DINPESA)
Page: 98

Article Type: Reseña

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