University of Tabriz Computational Methods for Differential Equations 2345-3982 14 2 2026 04 01 Infinitely many conservation laws, multi-wave solutions, and interactions for the (2+1)-dimensional complex modified Korteweg-de Vries system of equations 754 765 19401 10.22034/cmde.2024.62458.2753 EN Thilagarajah Mathanaranjan Department of Mathematics and Statistics, University of Jaffna, Sri Lanka. Journal Article 2024 07 12 In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries (cmKdV) system of equations. This system of equations is a generalization of the cmKdV equation in the (2+1)-dimension and has great significance in the fields of applied magnetism and nanophysics. On the basis of the Lax pair, infinitely many conservation laws are obtained. In addition, the multi-waves, homoclinic breather, rational, and interactions solutions of this equation are derived with the aid of logarithmic transformation and symbolic computation. For the suitable value of parameters, the 3D surfaces of obtained solutions have been plotted using Mathematica. https://cmde.tabrizu.ac.ir/article_19401_8990e049388034ffe087fd391750ae43.pdf