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The KdV and mKdV equations have many significant applications in the field of plasma physics and ocean dynamics. In this work, the traveling wave behavior of the newly proposed (2+1)-dimensional combined KdV–mKdV equation has been examined using two direct analytical approaches. The two variable G′G,1G-expansion method and generalized projective Riccati equation method are used to determine a variety of solitons and solitary waves for the governing model. The graphical observations are made for suitable choice of parametric values. The obtained results will provide useful insight in further explorations of the wave phenomena depicted by the considered equation.