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Integrable Vortex Dynamics and Complex Burgers' Equation
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165 b
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32.71
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Vortex motion as an essential ingredient of the§universe structure has attracted attention of§researchers and philosophers from ancient to modern§times. But the mathematical description of it has§begun in XIX century with works of Hermann Helmholtz§and Gustav Kirchoff.§This book is devoted to mathematical problem of§integrable vortex dynamics as a pole dynamics in§complex plane. Starting from basic notions of a fluid§motion the authors cover the Kirchhoff equations,§C-integrable models and time dependent holomorphic§Schrödinger equation. Intriguing relations with§motion of magnetic vortices, the Chern-Simons field§theory, Calogero-Moser systems, Burgers hierarchy§and the space-time noncommutativity are presented in§a systematic way. §The book is self consistent and pedagogically written§as an introduction to the subject for students at§undergraduate and graduate level from science and§engineering specialties. Also it could be a valuable§source for researchers in the field.
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