Nonlocal KdV equations

•One-soliton solution of the symmetrical Hirota-Satsuma (HS) system is obtained.•Integrable local and nonlocal reductions of the HS system are given.•All the reductions of the HS system give a kind of KdV equation; standard KdV, complex KdV, and nonlocal KdV equations.•By using the reduction formulas, one-soliton solutions of the local and nonlocal reduced equations are obtained. Writing the Hirota-Satsuma (HS) system of equations in a symmetrical form we find its local and new nonlocal reductions. It turns out that all reductions of the HS system are Korteweg-de Vries (KdV), complex KdV, and new nonlocal KdV equations. We obtain one-soliton solutions of these KdV equations by using the method of Hirota bilinearization.