P.H. Kersten – författare
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3 produkter
3 produkter
Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations
Inbunden, Engelska, 2000
1 589 kr
Skickas inom 10-15 vardagar
This is a detailed exposition of algebraic and geometrical aspects related to the theory of symmetries and recursion operators for nonlinear partial differential equations (PDE), both in classical and in super, or graded, versions. It contains an original theory of Frolicher-Nijenhuis brackets which is the basis for a special cohomological theory naturally related to the equation structure. This theory gives rise to infinitesimal deformations of PDE, recursion operators being a particular case of such deformations. Efficient computational formulas for constructing recursion operators are deduced and, in combination with the theory of coverings, lead to practical algorithms of computations. Using these techniques, previously unknown recursion operators (together with the corresponding infinite series of symmetries) are constructed. In particular, complete integrability of some superequations of mathematical physics (Korteweg-de Vries, nonlinear Schrodinger equations, etc.) is proved. It should be of interest to mathematicians and physicists specializing in geometry of differential equations, integrable systems and related topics.
Symmetries and Recursion Operators for Classical and Supersymmetric Differential Equations
Häftad, Engelska, 2010
1 589 kr
Skickas inom 10-15 vardagar
This book is a detailed exposition of algebraic and geometrical aspects related to the theory of symmetries and recursion operators for nonlinear partial differential equations (PDE), both in classical and in super, or graded, versions. It contains an original theory of Frolicher-Nijenhuis brackets which is the basis for a special cohomological theory naturally related to the equation structure. This theory gives rise to infinitesimal deformations of PDE, recursion operators being a particular case of such deformations. Efficient computational formulas for constructing recursion operators are deduced and, in combination with the theory of coverings, lead to practical algorithms of computations. Using these techniques, previously unknown recursion operators (together with the corresponding infinite series of symmetries) are constructed. In particular, complete integrability of some superequations of mathematical physics (Korteweg-de Vries, nonlinear Schrodinger equations, etc.) is proved. Audience: The book will be of interest to mathematicians and physicists specializing in geometry of differential equations, integrable systems and related topics.
534 kr
Skickas inom 10-15 vardagar
The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.