“Isomonodromy” solutions of equations of zero curvature

A detailed discussion is given of the analytic properties (explicit description, asymptotic representations, etc.) of a new class of solutions of completely integrable evolution systems – the class of “isomonodromy solutions” – introduced in recent works of a group of Japanese mathematicians: M. Sato, M. Jimbo, T. Miwa, and others. The role of the concept of an isomonodromy solution is demonstrated in such important questions of the theory of equations of zero curvature as finding the time asymptotics of solutions of corresponding Cauchy problems in the class of rapidly decreasing initial data.
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