On Nth-order rogue wave solution to nonlinear coupled dispersionless evolution equations

► A DT for the NLCDEE is constructed by the Darboux matrix method and the Lax pair. ► Based on the original DT, the generalized DT for the NLCDEE is derived via the Taylor expansion of the solution to the Lax pair. ► With the help of the generalized DT, the Nth-order rogue wave solutions to the NLCDEE are given out both graphically and analytically.