Abstract
In this paper, the thermophoretic motion equation based on Korteweg-de Vries is utilized to analyze new complexiton and soliton-like solutions. The homogenous balance approach is employed to generate auto-Backlund transformation of the concerned problem. This transformation is capitalized to extract abundant explicit and analytic solutions. Moreover, Hirota bilinear form of the concerned equation is taken under consideration to discover complexiton solutions via extended transform rational function approach. 3D visualization of the acquired solutions is also included to discuss its physical behavior.