Introduction to Multidimensional Integrable Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Multidimensional Integrable Equations write by B. G. Konopelchenko. This book was released on 2014-01-15. Introduction to Multidimensional Integrable Equations available in PDF, EPUB and Kindle.
Introduction to Multidimensional Integrable Equations
Introduction to Multidimensional Integrable Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Multidimensional Integrable Equations write by B.G. Konopelchenko. This book was released on 2013-06-29. Introduction to Multidimensional Integrable Equations available in PDF, EPUB and Kindle. 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.
Multidimensional Integral Equations and Inequalities
Multidimensional Integral Equations and Inequalities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Integral Equations and Inequalities write by B.G. Pachpatte. This book was released on 2011-07-26. Multidimensional Integral Equations and Inequalities available in PDF, EPUB and Kindle. Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.
Multidimensional Weakly Singular Integral Equations
Multidimensional Weakly Singular Integral Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Weakly Singular Integral Equations write by Gennadi Vainikko. This book was released on 2006-11-15. Multidimensional Weakly Singular Integral Equations available in PDF, EPUB and Kindle. The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.
Multidimensional Singular Integrals and Integral Equations
Multidimensional Singular Integrals and Integral Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Singular Integrals and Integral Equations write by S. G. Mikhlin. This book was released on 2014-07-10. Multidimensional Singular Integrals and Integral Equations available in PDF, EPUB and Kindle. Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.
