Abstract
A number of errors involving the expressions for the concepts, the algebraic operations, and the typographical in the derivation of the third-order evolution equations of Liu and Dingemans are pointed out and corrected. These modified equations are then extended to fourth-order with the stability analysis for uniform Stokes waves in which there exist certain fourth-order terms concerning the stability of finite depth waves, and to including the effects of ambient currents. These extensions result in a couple of equations, i.e. a general third-order evolution equation for the envelope of a modulated wave train with a current over an uneven bottom and an equation of the second-order (locked and free) long waves induced by the modulated wave train.
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