On the Effect of Intersection of Characteristics in a Two-Dimensional Massless Dirac Equation with Linear Potential and Localized Initial Condition

The Cauchy problem with a localized initial condition for the two-dimensional massless Dirac equation (describing quantum states in graphene [ 1 ]) with linear potential is considered. Applying the -Fourier transform with respect to the spatial variables to a solution , we can write, in some domains, a decomposition of of the form (an expansion in the modes ). The specific feature of this problem is that the phases and modes of this expansion have different form depending on the quantity . For , is constructed in the standard WKB form, where is constructed in the form of a series in powers of . For , is constructed by the Kucherenko method, using the Duhamel principle. DOI 10.1134/S1061920821020126