Internal-Wave Solitons of Fluids with Finite Depth

A nonlinear internal wave equation that describes stratified fluids with finite depth has been studied. N-soliton solutions were found through Hirota's method. Although the equation tends to either the Korteweg-de Vries equation or the Benjamin-Ono equation in the shallow- or deep-fluid limit, respectively, the N-soliton solutions obtained tend to the Korteweg-de Vries solitons in the shallow-fluid limit but do not tend to the Benjamin-Ono solitons in the deep-fluid limit. Therefore, there is no smooth transition from one kind of soliton to another with varying depth of the fluid.