Jump-defects in the nonlinear Schrodinger model and other non-relativistic field theories

Abstract

Recent work on purely transmitting 'jump-defects' in the sine-Gordon model and other relativistic field theories is extended to non-relativistic models. In all the cases investigated the defect conditions are provided by 'frozen' Backlund transformations and it is also shown via a Lax pair argument how integrability will be preserved in the presence of this type of defect. Explicit examples of the scattering of solitons by defects are given, and bound states associated with 'jump-defects' in the nonlinear Schrodinger model are described. Although the nonlinear Schrodinger model provides the principal example, some results are also presented for the Korteweg de Vries and modified Korteweg de Vries equations.

arXiv commentPublished version of the article with an extended introduction and some additional references

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• On the Inverse Scattering Method for Integrable PDEs on a Star Graph
• A multisymplectic approach to defects in integrable classical field theory
• The sine-Gordon model with integrable defects revisited
• Sigma models in the presence of dynamical point-like defects
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Defects in the discrete non-linear Schrodinger model
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• Dynamics of nonlinear-Schroedinger breathers in a potential trap
• Multisymplectic approach to integrable defects in the sine-Gordon model
• Grassmanian and Bosonic Thirring Models with Jump Defects
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• Darboux-Backlund transformations, dressing & impurities in multi-component NLS
• Classical impurities associated to high rank algebras
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• Type-II defects in the super-Liouville theory
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• Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models
• Defects in the supersymmetric mKdV hierarchy via Backlund transformations
• Backlund Transformation for Integrable Hierarchies: example - mKdV Hierarchy
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• Integrability of generalised type II defects in affine Toda field theory
• Generalized Backlund transformations for Affine Toda Hierarchies
• Transmission amplitudes from Bethe ansatz equations
• A note on gl_N type-I integrable defects
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