Evolution of Weak Discontinuities in Shallow Water Equations

Abstract

In this paper, we determine the critical time, when a weak discontinuity in the shallow water equations culminates into a bore. Invariance group properties of the governing system of partial differential equations (PDEs), admitting Lie group of point transformations with commuting infinitesimal operators, are presented. Some appropriate canonical variables are characterized that transform equations at hand to an equivalent form, which admits non-constant solutions. The propagation of weak discontinuities is studied in the medium characterized by the particular solution of the governing system