| 期刊全稱 | Analytic-Bilinear Approach to Integrable Hierarchies | | 影響因子2023 | L. V. Bogdanov | | 視頻video | http://file.papertrans.cn/157/156565/156565.mp4 | | 學(xué)科分類 | Mathematics and Its Applications | | 圖書封面 |  | | 影響因子 | The subject of this book is the hierarchies of integrable equations connected with the one-component and multi component loop groups. There are many publications on this subject, and it is rather well defined. Thus, the author would like t.o explain why he has taken the risk of revisiting the subject. The Sato Grassmannian approach, and other approaches standard in this context, reveal deep mathematical structures in the base of the integrable hi- erarchies. These approaches concentrate mostly on the algebraic picture, and they use a language suitable for applications to quantum field theory. Another well-known approach, the a-dressing method, developed by S. V. Manakov and V.E. Zakharov, is oriented mostly to particular systems and ex- act classes of their solutions. There is more emphasis on analytic properties, and the technique is connected with standard complex analysis. The language of the a-dressing method is suitable for applications to integrable nonlinear PDEs, integrable nonlinear discrete equations, and, as recently discovered, for t.he applications of integrable systems to continuous and discret.e geometry. The primary motivation of the author was to formalize the appr | | Pindex | Book 1999 |
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