Multi-soliton interactions of forced korteweg de vries equation with time-varying froude number

Abstract

Transcritical ows over uneven bottom topography are investigated, in the framework of the forced Korteweg de Vries (fKdV) equation. Pseudo-spectral method will be used to solve fKdV equations numerically to observe the effect of Froude number, especially for long time simulation. When the Froude number is constant, there is no collision between the uniform solitons due to the same amplitudes and speeds. However, two sets of solitary waves travelling upstream were discovered numerically when the Froude number varies. Various interaction patterns of the propagating upstream solitary waves which create a pairwise and two pairwise interactions were observed in the transcritical regime and are presented in various graphical outputs.