This paper primarily explores exponential soliton solutions, rational soliton solutions, and mixed exponential-rational soliton solutions for the (2+1)-dimensional nonlocal complex mKdV equation with \(r(x,y,t)=q^*(-x,y,t)\) . The collision behaviour of the three types of soliton solutions is focused on, and a detailed asymptotic analysis has been conducted. The main conclusions derived from the study are as follows. Firstly, it is observed that the collision between exponential soliton solutions in a continuous-wave background predominantly exhibit elastic interactions, accompanied by soliton phase shifts. The different collision types, including dark-dark, antidark-dark, dark-antidark, and antidark-antidark, are illustrated through graphical representations. Secondly, rational soliton solutions in a continuous-wave background demonstrate elastic collision without any phase shifts. Detailed discussions are provided on specific cases of antidark-dark, dark-antidark, and antidark-antidark interactions. The collision between exponential soliton solutions and rational soliton solutions are also observed to exhibit vanishing behaviour after interaction, which is explained with specific examples. Thirdly, the collision characteristics between the mixed exponential-rational soliton solutions are described. Finally, the stability of the solutions is studied with the aid of numerical simulations.
