Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics: Generalized Solitons and Hyperasymptotic Perturbation Theory (Mathematics and Its Applications, 442)

This is 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 that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.

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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describes A Class Of Waves That Radiate Away From The Core Of The Disturbance Yet Are Long-lived Nonlinear Disturbances. Also Discussed Are The Hyperasympototic Perturbation Theory And The Use Of Chebysev And Fourier Numerical Methods To Computer Solitary Waves. A Number Of Non-soliton Problems In Quantum Physics, Hydrodynamics, And Instability Theory Are Featured. The Final Chapters Examine Matched Asymptotic Expansions In The Complex Plane, The Small Denominator Problem In Stockes Expansions, Multiple Scale Expansions In Powers Of The Hyperbolic Secant And Tangent Functions, And Hyperasymptotic Perturbation Theory. Annotation C. By Book News, Inc., Portland, Or.

'... if a physical system is capable of supporting solitary wave motions then such motions will invariably arise from quite general excitations.'- T. Maxworthy (1980), pg. 52. The discover of nonlocal solitary waves is unknown and anonymous, but he or she lived in the dry north of Australia many millenia before the birth of writing. There, on the shores of the Gulf of Carpentaria, vast cylinders of cloud roll from northeast to southwest most mornings. Perhaps 300 meters in diameter, perhaps 500 meters above the ocean, these cylinders of cloud stretch from horizon to horizon. As the cloud evaporates on the trailing edge of the wave and condenses on the leading edge, the cylinder appears to roll backwards even as it propagates inland at perhaps 10-20 meters per second. Often, a whole train of cloud-cylinders propagates from Cape Yorke Penisula across the Gulf towards the southwest across modern Burketown, perhaps as much as 500 km inland into the Northern Territory. Modern-day Australians call it the'Morning Glory'. What the discover called it, so many centuries before the invention of hieroglyphics, the foundation of Ur and the coronation of the First Dynasty of China, we do not know. But unless he was very different from us, he felt awe. Physicists (Smith, 1988, and Rottman and Einaudi, 1!:!93) have identified the Morning Glory as a solitary wave.