The Significance of Nonlinearity in the Natural Sciences

. . . . . . . . . Frampton Nonlinear Deep Water Waves: A Physical Testing Ground for Solitons and Recurrence . . . . Lake Solitons as Particles, and the Effects of Perturbations . Kaup The Formulation of Variational Principles by Means of Clebsch Potentials .

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In accordance with the established tradition of these annual meetings under the aegis of Orbis Scientiae we have, this year, included the very important field of "The Significance of Non­ linearity in the Natural Sciences." We are pleased to join many scientists in recognizing the nonlinearity arising from the under­ lying interaction of all natural phenomena. It is tempting to say that in the long run things are nonlinear and that we shall have to design new techniques and methods to solve nonlinear equations. This year's Orbis Scientiae did include four sessions on nonlinear equations pertaining to elementary particle physics, molecular physics, fluid dynamics, and also to biology. Our Center intends to pursue the inclusions of these topics in its future Orbis Scientiae. Appreciation is extended to Mrs. Helga S. Billings, Mrs. Elva Brady, and Ms. Yvonne L. Leber for their skillful typing of the proceedings, which they have performed with great enthusiasm and dedication. The Editors v CONTENTS Some Recent Developments on Solitons in Two-Dimensional Field Theories 1 Andre Neveu Path Integral Quantization of Solitons. . . . . . . . . . 17 A. Jevicki Nontopological Solitons 39 R. Friedberg Vacuum Bubble Instantons 57 P. H. Frampton Nonlinear Deep Water Waves: A Physical Testing Ground for Solitons and Recurrence . . . . . 67 Henry C. Yuen and Bruce M. Lake Solitons as Particles, and the Effects of Perturbations . . . . 97 D. J. Kaup The Formulation of Variational Principles by Means of Clebsch Potentials .