Classical Integrable N=1 and $N= 2$ Super Sinh-Gordon Models with Jump Defects

Understand

The structure of integrable field theories in the presence of jump defects is discussed in terms of boundary functions under the Lagrangian formalism.

• Explicit examples of bosonic and fermionic theories are considered.
• In particular, the boundary functions for the N=1 and N=2 super sinh-Gordon models are constructed and shown to generate the Backlund transformations for its soliton solutions.
• As a new and interesting example, a solution with an incoming boson and an outgoing fermion for the N=1 case is presented.