Extension of the discrete KP hierarchy
A K Svinin · Journal of Physics A Mathematical and General · 2002
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 ).