Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics
Subtitle: Generalized Solitons and Hyperasymptotic Perturbation Theory
By: by John P. Boyd
Series: Mathematics and Its Applications -- 442; Mathematics and Its Applications -- 442
Publisher: Springer US
Published: 1998
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] :
Number of pages: 590
ISBN-13: 9781461376705; 9781461558255
Subjects: Mathematics; Global analysis (Mathematics); Geography
Description: Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics: Generalized Solitons and Hyperasymptotic Perturbation Theory represents the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves which radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances. Specific examples are provided in the areas of water waves, particle physics, meteorology, oceanography, fiber optics pulses and dynamical systems theory. For many species of nonlocal solitary waves the radiation is exponentially small in 1/epsilon where epsilon is a perturbation parameter, thus lying `beyond-all-orders'. A second theme is the description of hyperasymptotic perturbation theory and other extensions of standard perturbation methods. These methods have been developed for the computation of exponentially small corrections to asymptotic series. A third theme involves the use of Chebyshev and Fourier numerical methods to compute solitary waves. Special emphasis is given to steadily-translating coherent structures, a difficult numerical problem even today. A fourth theme is the description of a large number of non-soliton problems in quantum physics, hydrodynamics, instability theory and others where `beyond-all-order' corrections arise and where the perturbative and numerical methods described earlier are essential. Later chapters provide a thorough examination of matched asymptotic expansions in the complex plane, the small denominator problem in Poincaré-Linstead (`Stokes') expansions, multiple scale expansions in powers of the hyperbolic secant and tangent functions and hyperasymptotic perturbation theory. This book will be of special interest to applied mathematicians, fluid dynamicists in mechanical and aeronautical engineering, electrical engineers interested in fiber optics, quantum chemists and atomic and particle physicists.
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