Integrable Vortex Dynamics and Complex Burgers' Equation

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.

Autorentext

Zeynep N. Gürkan, MSc in Mathematics and research assistant at
Izmir Institute of Technology. Field of study: quantum computation.
Oktay K. Pashaev, Diploma in Physics - Moscow State University,
PhD - JINR, Dubna: Professor of Mathematics at Izmir Institute of
Technology, Turkey. Fields of study: integrable systems, solitons
and quantum physics.

Klappentext

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.