Integrable Vortex Dynamics and Complex Burgers' Equation
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Vortex motion as an essential ingredient of theuniverse structure has attracted attention ofresearchers and philosophers from ancient to moderntimes. But the mathematical description of it hasbegun in XIX century with works of Hermann Helmholtzand Gustav Kirchoff.This book is devoted to mathematical problem ofintegrable vortex dynamics as a pole dynamics incomplex plane. Starting from basic notions of a fluidmotion the authors cover the Kirchhoff equations,C-integrable models and time dependent holomorphicSchrödinger equation. Intriguing relations withmotion of magnetic vortices, the Chern-Si...
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 couldbe a valuable
source for researchers in the field.
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 couldbe a valuable
source for researchers in the field.
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