Edge states and chiral solitons in topological hall and Chern–Simons fields

The multi-component extension problem of the $(2+1)D$-gauge topological Jackiw–Pi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction $(2 + 1)D \to (1 + 1)D$ to Lagrangians with the Chern–Simons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with allowance for their interaction. With Hirota's method, an exact two-soliton solution is obtained, which is of interest in quantum information transmission systems due to the stability of their propagation. An asymptotic analysis $t\to\pm\infty$ of soliton-soliton interactions shows that there is no backscattering processes. We identify these solutions with the edge (topological protected) states — chiral solitons — in the multi-layer quantum Hall systems. By applying the Hirota bilinear operator algebra and a current theorem, it is shown that, in contrast to the usual vector solitons, the dynamics of new solutions (chiral vector solitons) has exclusively unidirectional motion. The article is published in the author's wording.