Classical integrable defects as quasi Bäcklund transformations

Abstract

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the "equations of motion" on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Backlund transformations. And although these equations are similar they are not exactly the same to the Backlund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

23 pages, Latex. Clarifying comments & references added; few typos corrected. Version to appear in NPB

References in corpus (6)

• Quantum and classical integrable sine-Gordon model with defect
• Lagrangian and Hamiltonian structures in an integrable hierarchy and space-time duality
• A multisymplectic approach to defects in integrable classical field theory
• Comments on defects in the a_r Toda field theories
• Multisymplectic approach to integrable defects in the sine-Gordon model
• A classical variant of the vertex algebra & the auxiliary linear problem

Cited by in corpus (9)

• Darboux-Backlund transformations, dressing & impurities in multi-component NLS
• Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models
• Defects in the supersymmetric mKdV hierarchy via Backlund transformations
• Integrability of generalised type II defects in affine Toda field theory
• Integrable crosscaps in classical sigma models
• Integrable Defects at Junctions within a Network
• Type II defects revisited
• On the nonlinear Schrödinger equation with a time-dependent boundary condition
• Time-dependent defects in integrable soliton equations