In the present paper, a systematic approach is presented for solution of two-dimensional massless Dirac equation with external electrostatic potential applied. This based on new - asymmetric form SUSY-like intertwining relations. It allows to build wide variety pairs SUSY-partner scalar potentials. If one them simple enough be solvable, its partner also solvable although it may have non-trivial...

A modified system of equations of electrodynamics has been obtained. Beside the Lagrangian one an alternative gauge-like formalism has been developed to introduce the toroid moment contributions in the equations obtained. The two potential formalism that was worked out by us earlier has been developed further where along with the two vector potentials we introduce two scalar potentials thus tak...

Some well known gauge scalar potential very often considered or used in the literature are investigated by means of classical Yang Mills equations for $SU(2)$ subgroups $N_c=3$. By fixing a particular shape potential, resulting vector potentials and corresponding color-charges sources found. adopting spherical coordinate system, it is shown that spherically symmetric solutions, only dependent o...

We consider scalar Born-Infeld type theories with arbitrary potentials V (T ) of a scalar field T . We find that for models with runaway potentials V (T ) the generic inhomogeneous solutions after a short transient stage can be very well approximated by the solutions of a Hamilton-Jacobi equation that describes free streaming wave front propagation. The analytic solution for this wave propagati...