Abstract
In this paper, generalized models for both (2+1)-dimensional cylindrical modified Korteweg–de Vries (cmKdV) equation with variable coefficients and (3+1)-dimensional variable coefficients cylindrical Korteweg–de Vries (cKdV) equation are studied by direct reduction method. A direct reduction to nonlinear ordinary differential equations in the form of Riccati equations obtained for the considered equations under some integrability conditions. The search for solutions for the reduced Riccati equations has yielded many Jacobi elliptic wave solutions, solitary and periodic wave solutions for both (2+1)-dimensional cmKdV and (3+1)-dimensional cKdV equations. Physical application for the obtained solutions as dust ion acoustic waves in plasma physics is given