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246073854
The Complex WKB Method for Nonlinear Equations I: Linear Theory (Progress in Mathematical Physics, 16)
Item #:
246073854
XCD 199
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We preserve this terminology in the case ImS(x) 0 and develop the method for a wide class of problems in mathematical physics.
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- This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich 5 -7, V. P. Lazutkin 76, A. A. Sokolov, 1. M. Ter- nov 113, J. Schwinger 107, 108, E. J. Heller 53, G. A. Hagedorn 50, 51, V. N. Bayer, V. M. Katkov 21, N. A. Chernikov 35 and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume 106 write in its preface: One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.
| Publisher | Birkhäuser |
| Publication date | October 6, 2012 |
| Edition | Reprint |
| Language | English |
| Print length | 311 pages |
| ISBN-10 | 3034896697 |
| ISBN-13 | 978-3034896696 |
| Item Weight | 15.7 ounces (445.1 grams) |
| Dimensions | 6.1 x 0.72 x 9.25 inches (15.5 x 1.8 x 23.5 cm) |
Who Should Buy?
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Advanced Researchers
Ideal for researchers focusing on nonlinear differential equations seeking in-depth theoretical insights and analytical techniques.
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Graduate Students
Beneficial for graduate students specializing in mathematical physics needing comprehensive understanding of complex WKB methods.
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Mathematicians
Suitable for mathematicians interested in the applications of nonlinear theories in mathematical physics and complex analysis.
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Casual Readers
Not suitable for casual readers lacking a strong background in mathematics and physics due to its complex nature.
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Mathematical Analysis Editorial Review
The Complex WKB Method for Nonlinear Equations I: Linear Theory, published by Birkhäuser on October 6, 2012, is an insightful resource comprising 311 pages that offers a deep dive into advanced mathematical physics concepts. This reprint edition, available in English, explores the implications of the WKB method in the context of nonlinear equations, making it a critical addition for scholars interested in theoretical frameworks. The book's dimensions and reasonable weight facilitate ease of handling, while the ISBN identifiers aid in locating this valuable text. Readers often find it an essential guide for understanding complex mathematical problems, enhancing their knowledge base in higher-level mathematics.
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Pros
- Comprehensive exploration of nonlinear equations
- Well-structured content for easy understanding
- Useful for advanced mathematics students
- Published by a reputable academic publisher
- Contains detailed theoretical frameworks
Cons
- Might be too advanced for beginners
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Features & Benefits
- Explore the Complex WKB Method for nonlinear equations.
- Understand asymptotic solutions in mathematical physics.
- Applicable to a broad range of linear and nonlinear equations.
- Preserves quantum mechanics terminology for effective learning.
- Addresses a crucial gap in obtaining general asymptotics.
- Develops computational procedures for complex phase fields.
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