Unified approach to strings and vortices with soliton solutions

Boundary RG flow associated with the AKNS soliton hierarchy

“…It is well to bear in mind that the classical Lund-Regge model, introduced in Ref. [55], is a representative of the AKNS soliton hierarchy. Notice also that if q = 0, then ǫ + = ǫ − and (179) turns into the integral equation which describes a vacuum boundary amplitude in the boundary sinh-Gordon model [35].…”

Quantum complex sine-Gordon model on a half line

“…We expect the non-CDD poles in (58) to be explained in terms of a on-shell triangle diagram as is the case for the a (1) n affine Toda theory. A full discussion can be found in [23].…”

“…Dorey and Hollowood noted that the CSG S-matrix is identical to the minimal a k−1 Smatrix which in turn can be recovered from the a (1) k−1 Affine Toda field theory (ATFT) when the parts involving the coupling constant are omitted. It is therefore reasonable to build our reflection matrix based on the proposed form for the particle reflection matrix of the boundary a (1) k−1 ATFT theory. In their paper Delius and Gandenberger [23] present a general form for the particle reflection matrix of the a (1) k−1 ATFT.…”

Symmetries in the third Painlevé equation arising from the modified Pohlmeyer-Lund-Regge hierarchy

“…Originally, the integrable Pohlmeyer-Lund-Regge system was derived in a study of the dynamics of relativistic vortices by Lund and Regge [12], and independently in an investigation of the nonlinear sigma model in field theory by Pohlmeyer [17]. In [8], Jimbo and Miwa showed that the third Painlevé equation is obtained through a similarity reduction from the Pohlmeyer-Lund-Regge equation.…”