Introduction to Multidimensional Integrable Equations : The Inverse Spectral Transform in 2+1 Dimensions

B. G. Konopelchenko

ISBN 10: 0306442205 / ISBN 13: 9780306442209

Published by Springer US, Springer US, 1993

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9780306442209

Bibliographic Details

Title: Introduction to Multidimensional Integrable ...

Publisher: Springer US, Springer US

Publication Date: 1993

Binding: Buch

Condition: Neu

About this title

Synopsis:

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.

Synopsis:

Focuses mainly on the mathematical aspects of higher-dimensional solitons found in a wide range of areas in physics, such as gravitation and field theory, plasma physics, and nonlinear optics and the multidimensional inverse spectral transform method, which allows investigations of nonlinear equations comparable to those of linear equations by the