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In the 25 years of its existence Soliton Theory has drastically expanded our understanding of "integrability" and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local cons

Solitons --- Differential equations, Nonlinear --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Numerical analysis --- Pulses, Solitary wave --- Solitary wave pulses --- Wave pulses, Solitary --- Connections (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Mathematics. --- Numerical solutions.