Unidirectional wave motions /

Description

Wave phenomena, with their multi-faceted aspects and diverse physical associations, sustain a considerable and continuing interest. It is well nigh impossible to survey, let alone assimilate, the accumulated findings over the centuries; and hence the acquisition of both perspective and procedural facility in this important sphere becomes ever more difficult. Students are conventionally introduced to wave theory as it bears on the particular subject matter of courses in mathematics, physics, and engineering, while the benefits of systematization in concept and technique remain unexplored for the most part. Books about wave theory in general are not so numerous, though some recent titles which manifest authoritative content and broad scope facilitate progress towards greater appreciation and technical mastery of the subject. This entrant to the published ranks aims to describe, in a comprehensive manner, the formulations and their consequent elaborations which have found demonstrable value in wave analysis; the deliberate focus on unidirectional waves permits a relatively simple mathematical development, without leaving significant gaps in methodology and capability. Since it is the full resources of mathematics which underlie successful dealings with all manner of wave problems, there are sufficient grounds for a detailed account of methods per se, encompassing both the active or contemporary representatives as well as those previously - and possibly again to be - judged useful. Sections of com­ parable size constitute the organizational framework of the book, marking a departure from the more typical arrangement of subject matter in chapters, and it is hoped that direct access to individual sections may enhance the utility of the work; problems are included, some taken (with permission) from examination papers set in The University of Cambridge, to display the nature of analytical solutions and further the ends of technical competence. An author’s indebtedness, in connection with an undertaking such as this, to information and benefit received from many sources cannot be adequately documented; special thanks are due, however, to T. T. Wu and F. G. Leppington for stimulating inputs, and to J. Schwinger for initially spotlight­ ing the elegance and versatility of applied mathematics. I am also grateful to Priscilla R. Feigen for an abundance of practical support and to the Office of Naval Research for prior material assistance.