LMS Workshop on  NONCOMMUTATIVE INTEGRABLE SYSTEMS,

Department of Mathematics

University of Glasgow, 25th -26th April 2008

 

Preseminar for graduate students:

 

            Jon Nimmo                                        Introduction to quasi-determinants

 

 

Workshop Programme:

 

 

            Mahmood-ul Hassan:                    Some aspects of the noncommutative principal chiral model

 

            Folkert Mueller-Hoissen:           A class of "partially linearizable" PDEs on associative algebras

 

                                                                        and

                 

                                                                        Lump solutions of the KP and the pseudodual chiral model hierarchy

 

            Olaf Lechtenfeld:                             The non-commutative sine-Gordon model

 

                                                                        and

 

                                                                        N=4 mechanics, WDVV equations and roots

 

 

 

 

Location: Room ???, Department of Mathematics.

 

Titles and abstracts: T.B.A.

 

Dr. Mueller-Hoissen 


Title: A class of "partially linearizable" PDEs on associative algebras

Abstract:
In the framework of bidifferential graded algebras we consider a class of
nonlinear partial differential (or difference) equations (with dependent
variable in an associative and typically noncommutative algebra), for which a
method exists generating exact solutions from a certain linear system of
PDEs. Special examples within this class are the self-dual Yang-Mills
equation and the  Kadomtsev-Petviashvili (KP) hierarchy (in an associative
algebra). All this is based on joint work with A. Dimakis.

Title: Lump solutions of the KP and the pseudodual chiral model hierarchy

Abstract:
As an application of results of my previous talk, in particular (ordinary and
anomalous) multi-lump solutions of the scalar KP-I hierarchy are recovered
(via matrix KP solutions) and corresponding solutions of the hierarchy of the 
"pseudodual chiral model" in 2+1 dimensions ("pseudodual" to Ward's
integrable chiral model) are obtained. This is essentially based on
Dimakis and Mueller-Hoissen, arXiv:0706.1373, arXiv:0712.3689.

 

 

 

Updated 3rd April 2008