Solution generating techniques for 2+I-dimensional nonlinear integrable systems
given by the integrability condition of linear problems (Lax pairs) are
presented. According to certain symmetries of these linear problems a distinction
between generalized Darboux and Darboux-Levi transformations
is made. In the 1+1-dimensional limit the link to twisted and untwisted
Kac-Moody algebras as prolongation algebras and the well-known N-soliton
Ansatz is discussed. It is shown that the Moutard theorem and the dromion
solutions for the Davey-Stewartson equation I are contained within this approach.
Moreover, the applicability of an extended version of the generalized
Darboux-Levi transformation to a Loewner-type system is demonstrated
which leads to localized soli tonic solutions of a 2+1-dimensional sine-Gordon
system (Konopelchenko-Rogers equations).
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.