Spectral Transform and Solitons PDF Download

Author: F. Calogero
Publisher: Elsevier
ISBN: 0080875343
Category : Mathematics
Languages : en
Pages : 533

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Spectral Transform and Solitons

Author: F. Calogero
Publisher: Pitman Publishing
ISBN:
Category : Mathematics
Languages : en
Pages : 292

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The volume contains the text of the invited lectures presented at the International Symposium on "Nonlinear Evolution Equations Solvable by the Inverse Spectral Transform", that took place at the Accademia dei Lincei in Rome from June 15 through June 18, 1977. It introduces an important mathematical technique based on the spectral transform and relevant to the solution of nonlinear evolution equations. These texts will be of particular value to theoretical physicists (in plasma, nonlinear optics, hydrodynamics, solid state and elementary particles); applied mathematicians interested in nonlinear evolution equations; and pure mathematicians interested in algebraic and differential geometry.

Author: F. Calogero
Publisher:
ISBN:
Category :
Languages : en
Pages : 257

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Author: Vladimir Gerdjikov
Publisher: Springer Science & Business Media
ISBN: 3540770534
Category : Science
Languages : en
Pages : 645

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This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Author: R.K. Bullough
Publisher: Springer Science & Business Media
ISBN: 3642814484
Category : Science
Languages : en
Pages : 403

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With contributions by numerous experts

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9401100179
Category : Mathematics
Languages : en
Pages : 507

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Book Description
Exactly one hundred years ago, in 1895, G. de Vries, under the supervision of D. J. Korteweg, defended his thesis on what is now known as the Korteweg-de Vries Equation. They published a joint paper in 1895 in the Philosophical Magazine, entitled `On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave', and, for the next 60 years or so, no other relevant work seemed to have been done. In the 1960s, however, research on this and related equations exploded. There are now some 3100 papers in mathematics and physics that contain a mention of the phrase `Korteweg-de Vries equation' in their title or abstract, and there are thousands more in other areas, such as biology, chemistry, electronics, geology, oceanology, meteorology, etc. And, of course, the KdV equation is only one of what are now called (Liouville) completely integrable systems. The KdV and its relatives continually turn up in situations when one wishes to incorporate nonlinear and dispersive effects into wave-type phenomena. This centenary provides a unique occasion to survey as many different aspects of the KdV and related equations. The KdV equation has depth, subtlety, and a breadth of applications that make it a rarity deserving special attention and exposition.

Author: Stig Lundqvist
Publisher: Springer Science & Business Media
ISBN: 1489920587
Category : Science
Languages : en
Pages : 482

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This volume is concerned with the theoretical description of patterns and instabilities and their relevance to physics, chemistry, and biology. More specifically, the theme of the work is the theory of nonlinear physical systems with emphasis on the mechanisms leading to the appearance of regular patterns of ordered behavior and chaotic patterns of stochastic behavior. The aim is to present basic concepts and current problems from a variety of points of view. In spite of the emphasis on concepts, some effort has been made to bring together experimental observations and theoretical mechanisms to provide a basic understanding of the aspects of the behavior of nonlinear systems which have a measure of generality. Chaos theory has become a real challenge to physicists with very different interests and also in many other disciplines, of which astronomy, chemistry, medicine, meteorology, economics, and social theory are already embraced at the time of writing. The study of chaos-related phenomena has a truly interdisciplinary charac ter and makes use of important concepts and methods from other disciplines. As one important example, for the description of chaotic structures the branch of mathematics called fractal geometry (associated particularly with the name of Mandelbrot) has proved invaluable. For the discussion of the richness of ordered structures which appear, one relies on the theory of pattern recognition. It is relevant to mention that, to date, computer studies have greatly aided the analysis of theoretical models describing chaos.

Author: W. Eckhaus
Publisher: Elsevier
ISBN: 0080871615
Category : Mathematics
Languages : en
Pages : 235

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The Inverse Scattering Transformation and The Theory of Solitons

Author: B.G. Konopelchenko
Publisher: Springer Science & Business Media
ISBN: 1489911707
Category : Science
Languages : en
Pages : 298

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Book Description
The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.

Author: Lokenath Debnath
Publisher: CUP Archive
ISBN: 9780521254687
Category : Mathematics
Languages : en
Pages : 376

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Book Description
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.