On nonclassical symmetries, Painlevé analysis and soliton solutions of three-coupled korteweg–de vries (KdV) system

Abstract The three coupled KdV system is investigated for exact solutions and Painlevé analysis. Exact solutions are examined through nonclassical symmetries via Bluman and Cole approach. Derived symmetries are generalizations of earlier obtained symmetries of the considered system. There is power series solution of the reduced ODEs of the examined system. Assuming the solutions in terms of Jacobi elliptic functions, some new soliton solutions of the system under consideration are obtained. These solutions are two-singular soliton, three-singular soliton, multi-soliton, multi-singular soliton, combined soliton, bright solion, dark soliton, and bell shaped soliton solutions. Further, graphical depiction of the exact solutions to the governing system. Using Kruskals method and symbolic software Maple, it is verified that the system has Painlevé property that represents integrability of the governing system.