In this book we have attempted to bring together much of the work that has been accomplished in the field which we loosely term: Solitons and the Inverse Scattering Transform. Usually, our procedure has been to explain the basic mathematical ideas by means of examples rather than by considering the most general situation. Attempts have been made to incorporate many of the important research papers into our bibliography. Unfortunately we are almost certain to have missed some relevant research articles. For this we apologize. Similarly, due to time considerations, we have not been able to include some of the very recent advances in this field. It should be remarked that this area of study is continuing to develop in a vigorous manner.

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