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Changing solitons in classical & quantum integrable defect and variable mass sine-Gordon model. (English) Zbl 1362.35250
Summary: Sine-Gordon (SG) models with position dependent mass or with isolated defects appear in many physical situations, ranging from fluxon or semi-fluxon in nonuniform Josephson junction to spin-waves in quantum spin chain with variable coupling or DNA solitons in the active promoter region. However such phenomena usually break the integrability of the model, allowing only numerical or perturbative result. We investigate two types of inhomogeneous sine-Gordon (SG) models: one with a variable mass and the other with a defect at the center and show integrability of both these models, in classical as well as in exact quantum level. The variable mass SG exhibits accelerating and shape changing exact solitons and can describe realistic problems at certain limits, while the defect SG possesses a rich class of exact solutions with creation or annihilation of solitons by the defect point. Based on our result theories for exact semi-fluxion solution in 0-\(\phi\)-Josephson junction is proposed.
MSC:
35Q51 Soliton equations
35C08 Soliton solutions
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