Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation
Abstract
We study integrable variable-mass sine-Gordon model (vmSG) with point defects. Using the Lax and Bäcklund-gauge formulations, we construct type-I and type-II defect matrices, derive the corresponding sewing conditions, and generate the bulk and defect contributions to an infinite hierarchy of conserved charges. The lowest members reduce to the standard sine-Gordon energy and momentum in the homogeneous limit, while for inhomogeneous backgrounds they define integrability-generated energy- and momentum-type quantities. Defect compatibility imposes matching conditions on the variable-mass functions across the defect. An analytical transmission factor z characterizes soliton transmission, topological conversion, and absorption/emission processes. We then deform the type-I sewing conditions by parameters α and β and derive the associated defect anomalies. Consistent one-soliton transmission is recovered for αβ=1, whereas for αβ≠ 1 parity-centered kink-kink and kink-antikink transmissions display vanishing lowest order integrated anomalies but no generic vanishing at higher order. Numerical simulations reproduce the integrable transmission/conversion regimes and show that non-integrable defects generate small residual disturbances and lowest order quasi-conserved charges, while quasi-conservation of the higher order charges remains unestablished. These results elucidate how exact defect integrability deforms into charge-dependent quasi-conservation and establish a framework for defect-controlled soliton transport in inhomogeneous media, with potential applications to nonuniform Josephson junctions, magnetic and nonlinear-optical systems, and effective molecular and DNA models.
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BibTeX
@misc{aguirre2026variablemass,
title = {{Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation}},
author = {A. R. Aguirre and H. Blas and H. F. Callisaya and M. C. de Oliveira},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.17211},
eprint = {2608.17211},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.17211},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation
AU - A. R. Aguirre
AU - H. Blas
AU - H. F. Callisaya
AU - M. C. de Oliveira
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.17211
UR - https://arxiv.org/abs/2608.17211
AB - We study integrable variable-mass sine-Gordon model (vmSG) with point defects. Using the Lax and Bäcklund-gauge formulations, we construct type-I and type-II defect matrices, derive the corresponding sewing conditions, and generate the bulk and defect contributions to an infinite hierarchy of conserved charges. The lowest members reduce to the standard sine-Gordon energy and momentum in the homogeneous limit, while for inhomogeneous backgrounds they define integrability-generated energy- and momentum-type quantities. Defect compatibility imposes matching conditions on the variable-mass functions across the defect. An analytical transmission factor z characterizes soliton transmission, topological conversion, and absorption/emission processes. We then deform the type-I sewing conditions by parameters α and β and derive the associated defect anomalies. Consistent one-soliton transmission is recovered for αβ=1, whereas for αβ≠ 1 parity-centered kink-kink and kink-antikink transmissions display vanishing lowest order integrated anomalies but no generic vanishing at higher order. Numerical simulations reproduce the integrable transmission/conversion regimes and show that non-integrable defects generate small residual disturbances and lowest order quasi-conserved charges, while quasi-conservation of the higher order charges remains unestablished. These results elucidate how exact defect integrability deforms into charge-dependent quasi-conservation and establish a framework for defect-controlled soliton transport in inhomogeneous media, with potential applications to nonuniform Josephson junctions, magnetic and nonlinear-optical systems, and effective molecular and DNA models.
ER -