AI 中文总结
该研究探讨带点缺陷的变质量正弦-戈登模型，通过构造缺陷矩阵、推导匹配条件与传输因子，揭示其可积性形变为准守恒性的规律，为非均匀介质的缺陷控制孤子传输提供框架。
AI 中文摘要
我们研究带点缺陷的可积变质量正弦-戈登模型（vmSG）。利用Lax和Bäcklund规范形式，我们构造了I型和II型缺陷矩阵，推导了相应的匹配条件，并生成了无限守恒荷层级的体贡献与缺陷贡献。最低阶项在均匀极限下退化为标准正弦-戈登模型的能量和动量，而在非均匀背景下，它们定义了由可积性产生的能量型和动量型量。缺陷兼容性对跨缺陷的变质量函数施加了匹配条件。解析传输因子z表征孤子传输、拓扑转换及吸收/发射过程。随后，我们通过参数α和β形变I型匹配条件，推导了相关的缺陷反常。当αβ=1时，可恢复一致的单孤子传输；而当αβ≠1时，以宇称为中心的扭结-扭结及扭结-反扭结传输显示最低阶积分反常消失，但高阶时一般不消失。数值模拟重现了可积传输/转换 regime，结果表明非可积缺陷会产生弱辐射尾及最低阶准守恒荷，而高阶荷的准守恒性仍未确立。这些结果阐明了精确缺陷可积性如何形变成为依赖于电荷的准守恒性，并建立了非均匀介质中缺陷控制孤子传输的框架，可应用于非均匀约瑟夫森结、磁性与非线性光学系统及有效分子和DNA模型。
英文摘要
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 $αβ\neq 1$ 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.
Comments49 pages, Latex. 7 Figs
