A fifth-order variable coefficient KdV equation arising from a fluid system

Starting from the model describing nonlinear phenomenon in atmosphere and ocean, a fifth order KdV equation with some arbitrary parameters is derived by using a long-wave approximation. Different to the usual treatment, the variable coefficient fifth KdV equation is obtained by the sum of the lower order term and the higher order term in the derivation procedure. Applying a novel travelling wave method to the derived model, it is found to possess many different and abundant travelling wave structures, such as the general solitary waves, the plateau soliton, the double-peak soliton, periodic waves, some type of soliton molecules (SMs) and two types of few-cycle-pulse (FCP) solitons.