Abstract
This paper investigates different kinds of exact solutions of variable-coefficients Chiral Schrödinger equation [Formula: see text]. In this equation, the fractional quantum Hall effect edge states are described. By the unified method, we successfully get the soliton, solitary and elliptic wave solutions. Through the [Formula: see text]-expansion and the exponential expansion methods, we acquire different traveling wave solutions. Using the extended [Formula: see text]-expansion method, we attain the Jacobi elliptic function solutions. So as to get more physical information about the exact solutions of VCCNLSE, [Formula: see text], density and contour maps are described.
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