Abstract
In this study, bottom topography with small-scale disturbances is incorporated into the first-order steady Korteweg–de Vries (KdV) type equation to reveal the detailed spatial variations of the wave profile on the bottom disturbed topography. Using the reductive perturbation method, theoretical solutions of this new equation are derived for two kinds of equilibrium wave profiles, i.e., the single soliton and the oscillation wave. The equilibrium theoretical wave profile becomes wide over a hump while turns narrow over a hole, which indicates that the wave profile has the stability adjustment capability to adapt to the disturbed bottom. The adaption of wave profiles to the bottom topography is piecewise, whose segmentation follows the variation of the uneven bottom disturbance. In addition, the increase of the water depth would decrease the adjustment of the wave profiles.
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