N-soliton solutions for the combined KdV–CDG equation and the KdV–Lax equation

The Hirota-Ito approach presented in [R. Hirota, M. Ito, Resonance of solitons in one dimension, J. Phys. Soc. Jpn. 52(3) (1983) 744–748] for extending fifth-order integrable equations with a nonvanishing boundary conditions to combined equations is used in this work. The generalized fifth-order Caudrey-Dodd-Gibbon (CDG) and Lax equations are extended to combined integrable equations. The Hirota’s bilinear method is used to derive multiple-soliton solutions for the extended KdV–CDG and KdV–Lax equations.