A Study of Different Wave Structures of the $(2 + 1)$-dimensional Chiral Schrödinger Equation

In the present paper, the authors are interested in studying a famous nonlinear PDE re- ferred to as the $(2 + 1)$-dimensional chiral Schrödinger (2D-CS) equation with applications in mathematical physics. In this respect, the real and imaginary portions of the 2D-CS equation are firstly derived through a traveling wave transformation. Different wave structures of the 2D-CS equation, classified as bright and dark solitons, are then retrieved using the modified Kudryashov (MK) method and the symbolic computation package. In the end, the dynamics of soliton solutions is investigated formally by representing a series of 3D-plots.