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 Nth 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.

Automated summary

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