Anning Hu - Böcker

GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical ?bre etc., and has many applications in science and technology (like optical signal communication). On the other hand, it gives many e?ective methods ofgetting explicit solutions of nonlinear partial di?erential equations. Therefore, it has attracted much attention from physicists as well as mathematicians. Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems. Getting explicit solutions is usually a di?cult task. Only in c- tain special cases can the solutions be written down explicitly. However, for many soliton equations, people have found quite a few methods to get explicit solutions. The most famous ones are the inverse scattering method,B.. acklund transformation etc. The inverse scattering method is based on the spectral theory of ordinary di?erential equations. The Cauchyproblemofmanysolitonequationscanbetransformedtosolving a system of linear integral equations. Explicit solutions can be derived when the kernel of the integral equation is degenerate.The B.. ac .. klund transformation gives a new solution from a known solution by solving a system of completely integrable partial di?erential equations. Some complicated "nonlinear superposition formula" arise to substitute the superposition principlein linear science.

In view of the dramatically increased interest in the study of grain boundaries during the past few years, the Physical Metal­ lurgy Committee of The Institute of Metals Division of The Metal­ lurgical Society, AIME, sponsored a four-session symposium on the NATURE AND BEHAVIOR OF GRAIN BOUNDARIES, at the TMS-AIME Fall Meeting in Detroit, Michigan, October 18-19, 1971. The main ob­ jectives of this symposium were to examine the more recent develop­ ments, theoretical and experimental, in our understanding of grain boundaries, and to stimulate further studies in these and related areas. This volume contains most of the papers presented at the Symposium. It is regrettable that space limitations allow the inclusion of only four of the unsolicited papers, in addition to thirteen invited papers. The papers are grouped into three sections according to their major content: STRUCTURE OF GRAIN BOUNDARIES, ENERGETICS OF GRAIN BOUNDARIES, and GRAIN BOUNDARY MOTION AND RELATED PHENOMENA. Grain boundaries, or crystal interfaces, have been of both academic and practical interest for many years. An early seminar on "Metal Interfaces" was documented in 1952 by ASM. The Fourth Metallurgical Colloquium held in France, 1960, had a broad coverage on "Properties of Grain Boundaries". More recently the Australian Institute of Metals sponsored a conference on interfaces, with the proceedings being published by Butterworths in 1969.

GU Chaohao The soliton theory is an important branch of nonlinear science. On one hand, it describes various kinds of stable motions appearing in - ture, such as solitary water wave, solitary signals in optical ?bre etc., and has many applications in science and technology (like optical signal communication). On the other hand, it gives many e?ective methods ofgetting explicit solutions of nonlinear partial di?erential equations. Therefore, it has attracted much attention from physicists as well as mathematicians. Nonlinearpartialdi?erentialequationsappearinmanyscienti?cpr- lems. Getting explicit solutions is usually a di?cult task. Only in c- tain special cases can the solutions be written down explicitly. However, for many soliton equations, people have found quite a few methods to get explicit solutions. The most famous ones are the inverse scattering method,B.. acklund transformation etc. The inverse scattering method is based on the spectral theory of ordinary di?erential equations. The Cauchyproblemofmanysolitonequationscanbetransformedtosolving a system of linear integral equations. Explicit solutions can be derived when the kernel of the integral equation is degenerate.The B.. ac .. klund transformation gives a new solution from a known solution by solving a system of completely integrable partial di?erential equations. Some complicated "nonlinear superposition formula" arise to substitute the superposition principlein linear science.