# the Toda Lattice hierarchy of B and C type

In the K.Ueno and K.Takasaki's paper Toda Lattice hierarchy", advanced sdudies in pure mathematics 4(1984),pp1-95, they mentioned the Toda Lattice hierarchy of B and C type(we denote BTL and CTL hierarchies).In their paper, the bilinear relation for BTL and CTL hierarchies are almost the same as the one for Toda Lattice hierarchy except with the even time flows being zero( see eq.2.4.1 in reference).

My question is as follows:

1. Since the KP and TL hierarchies are almost the same (see Mark Adler et al's paper Comm.math.Phys.171,547-588(1995)), and considering the great difference between the bilinear relations for BKP and KP hierarchies(see E.Date,Jimbo,et al's paper,Transformation groups for soltion equations), why BTL and TL lattice hierarches are almost the same? Is there something wrong?

2. Can the BTL and CTL hierarchies have the fay like identities just as the KP and BKP hierarchies(see H.F.Shen and M.H.Tu's paper,arxiv:0811.1469)

3. why the literatures for the BTL and CTL hierarchies are so few? is there someting difficult in studying them?

thanks

• After 11 hours with no response, it seems likely that a bit more information would increase your chance of getting a response. – Pete L. Clark Apr 29 '10 at 18:52

## 1 Answer

I suggest

http://arxiv.org/abs/nlin.SI/0608018

as a first step