2001/10/19 by A. K. Svinin, A K Svinin
Computer Science · Physics and Astronomy · #Advanced Algebra and Logic #Algebra over a field #Analytical hierarchy #Extension (predicate logic) #Fuzzy Logic and Control Systems #Hierarchy #Rough Sets and Fuzzy Logic #Term (time) #nlin.SI
paper · pdf · doi:10.1088/0305-4470/35/8/317
LaTeX, 16 pages
arxiv created 2001/10/19 · openalex publication_date 2002/02/18 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we discuss possible generalizations of the discrete KP (Toda lattice) hierarchy. As a result, we introduce the integrable hierarchy which can be considered as the proper extension of the discrete KP hierarchy. Such extension forces us to introduce an infinite number of additional multi-times t ( n ) ≡( t ( n ) 1 ≡ x ( n ) , t ( n ) 2 ,...), n ⩾2, whereas ordinary discrete KP is relevant to t (1) . It is shown that any subsystem of extended discrete KP attached to multi-time t ( n ) is in fact equivalent to a bi-infinite sequence of continuous KP hierarchies whose Lax operators are glued together by compatible `gauge' transformations. This paper can be thought of as a natural continuation and generalization of our previous paper (Svinin A K 2001 J. Phys. A: Math. Gen. 34 10559-68 ).