The aim of this work is to supply a collection of problems together with their detailed solutions, which should prove to be valuable to students as well as to research workers in the fields mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. All relevant definitions are given. Volume I presents the introductory problems for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover most of the new fields in theoretical and mathematical physics such as Lax representation, Backlund transformation, soliton equations, Lie algebra valued differential forms, Hirota technique, Painleve test, the Bethe ansatz, the Yang-Baxter relation, chaos and fractals.
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