关于具有无穷远处非零位势的Dirac、动力学Dirac及Dirac–Weyl系统的新显式解类、其性质与应用
On new classes of explicit solutions of Dirac, dynamical Dirac and Dirac--Weyl systems with non-vanishing at infinity potentials, their properties and applications
AI总结：
本文利用GBDT版本的Bäcklund-Darboux变换，构造了具有无穷远处非零位势的自伴与斜自伴Dirac系统、动力学Dirac及Dirac–Weyl系统的广泛新显式解，并推导了Weyl–Titchmarsh函数。
摘要：
我们将GBDT版本的Bäcklund-Darboux变换应用于构造自伴与斜自伴Dirac系统、动力学Dirac系统及Dirac–Weyl系统的广泛新显式解类。也就是说，我们构造了具有无穷远处非零位势的系统的显式解。特别地，处理了阶梯状位势和位势幂增长的情形。关键在于（尤其是对动力学情形），在GBDT中使用广义矩阵特征值代替通常的特征值（且这些矩阵特征值不一定是对角矩阵）。讨论了Dirac–Weyl系统与石墨烯理论的联系。推导了Weyl–Titchmarsh函数的显式表达式。
英文摘要：
Our GBDT version of Bäcklund-Darboux transformation is applied to the construction of wide classes of new explicit solutions of self-adjoint and skew-self-adjoint Dirac systems, dynamical Dirac and Dirac--Weyl systems. That is, we construct explicit solutions of systems with non-vanishing at infinity potentials. In particular, the cases of steplike potentials and power growth of potentials are treated. It is essential (especially, for dynamical case) that the generalised matrix eigenvalues are used in GBDT instead of the usual eigenvalues (and those matrix eigenvalues are not necessarily diagonal). The connection of Dirac--Weyl system with graphene theory is discussed. Explicit expressions for Weyl--Titchmarsh functions are derived.
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