The dynamics of surface wave propagation based on the Benjamin Bona Mahony equation.

Modulation instability is one of the consequences of the water medium's inclination. It causes surface water waves to run into phenomena of splitting and merging in their propagation. An increase in wave amplitude follows this phenomenon, which can encourage the appearance of extreme waves.

Discrete solitons in electromechanical resonators.

We consider a particular type of parametrically driven discrete Klein-Gordon system describing microdevices and nanodevices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrödinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein-Gordon system through the discrete Schrödinger equation.