A Two-Dimensional Map Derived From An Ordinary Difference Equation of mKdV and Its Properties

The discrete modified Korteweg–de Vries (mKdV) is a class of discrete integrable systems that may be distinguished as integrable partial difference equations (PΔE) and integrable ordinary difference equations (OΔE). By considering traveling wave solutions, the OΔE mKdV can be obtained from PΔE mKdV. Meanwhile, a mapping can be constructed from an OΔE mKdV. In this paper, we will focus on producing a new map using a process (replacement), the interchange of a single parameter, and an integral and investigate its properties.