Defects in the supersymmetric mKdV hierarchy via Backlund transformations

Abstract

The integrability of the $\mathcal{N}=1$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation is performed by using essentially two methods: the Bäcklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the Bäcklund equations in components for the first few flows of the hierarchy, namely $t_3$ and $t_5$. Secondly, the supersymmetric extension of the Bäcklund transformation in the superspace formalism is constructed for those flows. Finally, this super Bäcklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.

40 pages. Some comments and references added. Version accepted for publication in JHEP

References in corpus (15)

• Quantum and classical integrable sine-Gordon model with defect
• On purely transmitting defects in affine Toda field theory
• A multisymplectic approach to defects in integrable classical field theory
• Integrablility of a Classical $N=2$ Super Sinh-Gordon Model with Jump Defects
• The sine-Gordon model with integrable defects revisited
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Sigma models in the presence of dynamical point-like defects
• Soliton Solutions for the Super mKdV and sinh-Gordon Hierarchy
• Permutability of Backlund Transformation for N=1 Supersymmetric Sinh-Gordon
• Grassmanian and Bosonic Thirring Models with Jump Defects
• Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model
• N=1 super sinh-Gordon model with defects revisited
• Backlund Transformation for Integrable Hierarchies: example - mKdV Hierarchy
• Integrability of generalised type II defects in affine Toda field theory
• Defect fusing rules in affine Toda field theory

Cited by in corpus (1)

• Quantum anomalies in A^{(1)}_r Toda theories with defects