Soliton equations and Hamiltonian systems
L. A. Dickey
World Scientific
Dickey (mathematics, U. of Oklahoma) provides a detailed description of solitons, which have numerous applications in mechanics and physics. The new edition contains several additions and modifications including discussion of the Zakharov-Shabat matrix hierarchy with rational dependence on a spectral parameter, and its relationship to isomonodromic deformations. Overall, the emphasis of the second edition is on hierarchies of integrable equations rather than individual equations. The second edition also contains a new preface by the author. Chapters include Hamiltonian structure of the GD hierarchies, Kupershmidt-Wilson Theorem and modified KdV and GD, and tau functions of matrix hierarchies.