论文标题
在新的狄拉克，动态狄拉克和狄拉克的新的明确解决方案中 - 无限潜力，其属性和应用
On new classes of explicit solutions of Dirac, dynamical Dirac and Dirac--Weyl systems with non-vanishing at infinity potentials, their properties and applications
论文作者
论文摘要
我们的GBDT版本的Bäcklund-darboux变换应用于构建一类新的自我偶像和偏斜的新型解决方案，偏向自我的狄拉克系统，动态狄拉克和dirac-weyl Systems。也就是说，我们构建了在无穷大潜力下具有非变化的系统的明确解决方案。特别是，治疗了型潜力和电势的功率增长的病例。至关重要的是（尤其是对于动态情况），在GBDT中使用了广义矩阵特征值，而不是通常的特征值（并且那些矩阵特征值不一定是对角线）。讨论了Dirac-Weyl系统与石墨烯理论的联系。得出了Weyl-titchmarsh功能的显式表达式。
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.
