Abstract
Abstract In mathematics and physics, one of the main tasks is to relate differential geometry and non-linear differential equations, which means that the study of particular cases of subvarieties, curves, and surfaces are of great importance. Soliton surfaces associated with the integrable system play an essential role in many problems with the physical application. In this paper, we study the complex modi ed Korteweg de Vries (cmKdV) equation. It is well known that the cmKdV equation is a very important integrable equation. We present the relationship between an integrable system and soliton surfaces and namely Lax representation of the cmKdV equation was used to obtain the rst and second fundamental forms, surface area and curvature.