Abstract
We compare the motion of solitary surface waves resulting from two similar but slightly different approaches. In the first approach, the evolution of soliton surface waves moving over the uneven bottom is obtained using single wave equations, whereas, in the second approach, the evolution of the same initial conditions results from the solution of the coupled set of Boussinesq equations for the same system of Euler equations. We discuss four physically relevant cases of relationships among small parameters α, β, δ. For the flat bottom, these cases are modeled by Korteweg-de Vries equation (KdV), extended KdV (KdV2), fifth-order KdV, and Gardner equation. In all studied cases, the influence of the bottom variations on the amplitude and velocity of a surface wave calculated from Boussinesq equations is substantially more significant than that obtained from single wave equations.
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