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In this work we develop two new (2+1) and (3+1)-dimensional KdV equations with constant and time-dependent coefficients. The integrability of each established equation is investigated via using the Painlevé test. We also examine the compatibility conditions to ensure the integrability for each model. The Hirota's method is used to derive multiple-soliton solutions for these equations. We establish the dispersion relation and the phase shifts for each case.