For more than 20 years, the Korteweg-de Vries equation has been intensively explored from mathematical point of view. Regarding control theory, when adding an internal force term in this equation, it is well known that exponentially stable a bounded domain. In work, we propose weak forcing mechanism, with lower cost already existing literature, to achieve result global exponential stability equ...

(Received ?? and in revised form ??) It is well-known that transcritical flow over a localised obstacle generates upstream and downstream nonlinear wavetrains. The flow has been successfully modeled in the framework of the forced Korteweg-de Vries equation, where numerical and asymptotic analytical solutions have shown that the upstream and downstream nonlinear wavetrains have the structure of ...

Nonlinear long wave propagation in a medium with periodic parameters is considered in the framework of a variable-coefficient Korteweg-de Vries equation. The characteristic period of the variable medium is varied from slow to rapid, and its amplitude is also varied. For the case of a piecewise constant coefficient with a large scale for each constant piece, explicit results for the damping of a...

Transcritical flow over a localised obstacle generates upstream and downstream nonlinear wavetrains. In the weakly nonlinear long-wave regime, this flow has been modeled with the forced Korteweg-de Vries equation, where numerical simulations and asymptotic solutions have demonstrated that the upstream and downstream nonlinear wavetrains have the structure of unsteady undular bores, connected by...