Bilinear-form and similarity-reduction visit to a variable-coefficient generalized dispersive water-wave system concerning Acta Mech. 233, 2527 and 233, 2415

Getting enthusiastic from two Acta Mech. water-wave advances, this Letter proposes to visit a variable-coefficient generalized dispersive water-wave system for certain long-weakly nonlinear and weakly-dispersive surface waves of variable depth in a shallow water. In regard to the height modeling the deviation from the equilibrium position of the water and to the surface velocity of water waves along a horizontal direction, we symbolically compute out the following: (1) bilinear forms, the same as those published but by way of a different method; (2) similarity reductions, each of which to a known ordinary differential equation. Results are related to the fluid density, velocity and viscosity.