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Author: Peter Cornelis Schuur
Publisher: Springer
ISBN: 3540473874
Category : Science
Languages : en
Pages : 188
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Book Description
Author: Peter Cornelis Schuur
Publisher: Springer
ISBN: 3540473874
Category : Science
Languages : en
Pages : 188
Get Book Here
Book Description
Author: Peter Cornelis Schuur
Publisher:
ISBN: 9783662204375
Category :
Languages : en
Pages : 192
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Book Description
Author: Mark J. Ablowitz
Publisher: Cambridge University Press
ISBN: 1139503480
Category : Mathematics
Languages : en
Pages : 363
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Book Description
The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
Author: Spyridon Kamvissis
Publisher: Princeton University Press
ISBN: 069111482X
Category : Mathematics
Languages : en
Pages : 281
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Book Description
Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.
Author: M. V. Karasev
Publisher: American Mathematical Soc.
ISBN: 9780821833360
Category : Asymptotic symmetry (Physics)
Languages : en
Pages : 298
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Book Description
The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.
Author: O. Axelsson
Publisher: Elsevier
ISBN: 0080871585
Category : Mathematics
Languages : en
Pages : 399
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Book Description
Analytical and Numerical Approaches to Asymptotic Problems in Analysis
Author: Mikhail V. Fedoryuk
Publisher: Springer Science & Business Media
ISBN: 3642580165
Category : Mathematics
Languages : en
Pages : 370
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Book Description
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
Author: F. de Kerf
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 196
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Book Description
Author: Hans G. Kaper
Publisher: CRC Press
ISBN: 1482277069
Category : Mathematics
Languages : en
Pages : 283
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Book Description
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Author:
Publisher:
ISBN: 9780821821091
Category : Differential equations, Nonlinear
Languages : en
Pages : 285
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Book Description
