Investigation on a nonisospectral fifth-order Korteweg-de Vries equation generalized from fluids

In this paper, a nonisospectral fifth-order Korteweg-de Vries equation generalized from fluids is investigated. With symbolic computation, such equation is transformed into its bilinear form through a proposed dependent variable transformation with one more parameter than those in the existing literature. N-soliton solutions, Bäcklund transformation, and Lax pair in the explicit forms are constructed. Based on the above results, the characteristic-line method is applied to discuss the features of the solitons for the nonisospectral problem, i.e., the controllable solitonic velocities and widths. Four types of solitonic structures with the different solitonic velocities, widths, amplitudes, and backgrounds are also illustrated.