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arXiv · 2608.17211

Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation

A. R. Aguirre·H. Blas·H. F. Callisaya·M. C. de Oliveira
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Abstract

We study integrable variable-mass sine-Gordon model (vmSG) with point defects. Using the Lax and B\"acklund-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 $\alpha$ and $\beta$ and derive the associated defect anomalies. Consistent one-soliton transmission is recovered for $\alpha \beta =1$, whereas for $\alpha \beta \neq 1$ 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 weak radiative tails 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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A. R. Aguirre, H. Blas, H. F. Callisaya, M. C. de Oliveira. 2026-08-17. Variable-mass sine-Gordon with point defects: integrability, soliton transmission, and quasi-conservation. https://arxiv.org/abs/2608.17211

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