Multisoliton and rational solutions for the extended fifth-order KdV equation in fluids with self-consistent sources

Based on the high-order restricted flows of the extended fifth-order KdV (efKdV) equation, the efKdV equation with self-consistent sources (efKdVESCS) is presented and its Lax pair is constructed. Two types of $N$th Darboux transformations for the efKdVESCS are constructed. By using Darboux transformations, some types of solutions including one-soliton, two-soliton, and rational solution are explicitly obtained.