Non Abelian Nonlinear Evolution Equations & Baecklund Transformations

Structural Properties of Non Abelian Nonlinear Evolution Equationsare studied. Specifically, third order Non Abelian Nonlinear Evolution Equations, such as potential Korteweg deVries (pKdV), Korteweg deVries (KdV) as well as different versions of modified Korteweg deVries (mKdV), and the Korteweg deVries interacting soliton and Korteweg deVries singuarity manifold equations and links among them are studied [1,2,3]. The Bäcklund Transformations connecting all these equations are depicted in aBäcklund Chart. It represents an extension of the Bäcklund Chart in [4] obtained in the case of nonlinear evolution equations in an unknown real valued function. Also in the non Abelian case all the studied equations are proved to admit a hereditary recursion operator. Hence the corresponding hierarchies are constructed. Results on non Abelian Burgers equations and hierarchies are also mentioned [5,6].