Similarity analysis of long wave equations with variable bottom friction (Q880468)

Summary: Long wave equations propagating along an open channel with bottom friction are considered. The equations are cast into a non-dimensional form. Scaling and translational symmetries of the equations are calculated for the cases of constant bottom friction coefficient and variable bottom friction coefficient. Using the symmetries, the partial differential equations are transformed into ordinary differential equations. Analytical and numerical solutions of the ordinary differential equations are found and solutions are compared with each other.