Solitons in the Fifth-Order KdV Equation with a Perturbation

The fifth-order KdV equation with a perturbation term is naturally consistent with the shallow-water wave model. In this study, the leading-order asymptotic solution of the perturbed fifth-order KdV equation was derived using the multi-scale perturbation expansion method. Furthermore, the asymptotic solution was reconsidered from the perspective of conservation laws, and consistent results were obtained. In addition, the numerical solution of the slowly varying solitary wave asymptotic solution was obtained using the Fourier spectral method under appropriate initial conditions to better understand its dynamic behavior. These results enrich research on fluid dynamics.