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Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics

Generalized Solitons and Hyperasymptotic Perturbation Theory

  • John P. Boyd

Part of the Mathematics and Its Applications book series (MAIA, volume 442)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Overview

    1. Front Matter
      Pages 1-1
    2. John P. Boyd
      Pages 3-28
  3. Analytical Methods

  4. Numerical Methods

    1. Front Matter
      Pages 139-139
    2. John P. Boyd
      Pages 141-171
    3. John P. Boyd
      Pages 172-223
  5. Applications

  6. Radiative Decay & other Exponentially Small Phenomena

    1. Front Matter
      Pages 431-431
    2. John P. Boyd
      Pages 455-478
    3. John P. Boyd
      Pages 479-481
  7. Back Matter
    Pages 482-596

About this book

Introduction

" . . . 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.

Keywords

algorithms differential equation dynamics numerical methods quantum physics stability waves

Authors and affiliations

  • John P. Boyd
    • 1
  1. 1.University of MichiganAnn ArborUSA

Bibliographic information