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With a balanced combination of longer survey articles and shorter,
peer-reviewed research-level presentations on the topic of
differential and difference equations on the complex domain, this
edited volume presents an up-to-date overview of areas such as WKB
analysis, summability, resurgence, formal solutions, integrability,
and several algebraic aspects of differential and difference
equations.
The discovery of a virtual turning point truly is a breakthrough in
WKB analysis of higher order differential equations. This monograph
expounds the core part of its theory together with its application
to the analysis of higher order Painleve equations of the
Noumi-Yamada type and to the analysis of non-adiabatic transition
probability problems in three levels. As M.V. Fedoryuk once
lamented, global asymptotic analysis of higher order differential
equations had been thought to be impossible to construct. In 1982,
however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a
remarkable paper in the Journal of Mathematical Physics indicating
that the traditional Stokes geometry cannot globally describe the
Stokes phenomena of solutions of higher order equations; a new
Stokes curve is necessary.
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