Coupled KdV equations derived from two-layer fluids

Some types of coupled Korteweg de-Vries (KdV) equations are derived from a two-layer fluid system. In the derivation procedure, an unreasonable y-average trick (usually adopted in the literature) is removed. The derived models are classified by means of the Painlevé test. Three types of τ-function and multiple soliton solutions of the models are explicitly given via the exact solutions of the usual KdV equation. It is also discovered that a non-Painlevé integrable coupled KdV system can have multiple soliton solutions.