Weakly nonassociative algebras, Riccati and KP hierarchies

Details Weakly nonassociative algebras, Riccati and KP hierarchies Weakly nonassociative algebras, Riccati and KP hierarchies

2007-01-04

arxiv.org/abs/nlin/0701010v4

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, second version: LaTeX problem with L's in section 5 resolved, third version: example 2 in section 3 added, some mino

Scientific paper

It has recently been observed that certain nonassociative algebras (called "weakly nonassociative", WNA) determine, via a universal hierarchy of ordinary differential equations, solutions of the KP hierarchy with dependent variable in an associative subalgebra (the middle nucleus). We recall central results and consider a class of WNA algebras for which the hierarchy of ODEs reduces to a matrix Riccati hierarchy, which can be easily solved. The resulting solutions of a matrix KP hierarchy then determine (under a rank 1 condition) solutions of the scalar KP hierarchy. We extend these results to the discrete KP hierarchy. Moreover, we build a bridge from the WNA framework to the Gelfand-Dickey formulation of the KP hierarchy.

Affiliated with

Also associated with

No associations

Rating

Weakly nonassociative algebras, Riccati and KP hierarchies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Weakly nonassociative algebras, Riccati and KP hierarchies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weakly nonassociative algebras, Riccati and KP hierarchies will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-310445