Title
Soliton Equations and their AlgebroGeometric Solutions: Volume 1, (1+1)Dimensional Continuous Models (Cambridge Studies in Adv,New
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This book is about algebrogeometric solutions of completely integrable nonlinear partial differential equations in (1+1)dimensions; also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sineGordon, and CamassaHolm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebrogeometric solutions in the stationary and timedependent contexts is provided. The formalism presented includes trace formulas, Dubrovintype initial value problems, BakerAkhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces).
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