A note on exact particular solutions of the generalized shallow-water equations

Odulo, Anatoly B.

doi:10.1090/qam/1811098

Author: Anatoly B. Odulo
Journal: Quart. Appl. Math. 59 (2001), 143-145
MSC: Primary 35Q35; Secondary 35F20, 76B70
DOI: https://doi.org/10.1090/qam/1811098
MathSciNet review: MR1811098
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This note presents a set of systems of two first-order quasi-linear partial differential equations, which can be reduced to the shallow-water equations. This set includes equations describing a two-layered fluid flow.

Peter G. Baines, Topographic effects in stratified flows, Cambridge Monographs on Mechanics, Cambridge University Press, Cambridge, 1995. MR 1354393
Julio Gratton and Claudio Vigo, Self-similar gravity currents with variable inflow revisited: plane currents, J. Fluid Mech. 258 (1994), 77–104. MR 1263151, DOI https://doi.org/10.1017/S0022112094003241
Anatoly Odulo, A method of obtaining exact particular solutions of a system of two first-order quasilinear partial differential equations, Quart. J. Mech. Appl. Math. 44 (1991), no. 2, 323–331. MR 1104876, DOI https://doi.org/10.1093/qjmam/44.2.323
G. B. Whitham, Linear and nonlinear waves, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. Pure and Applied Mathematics. MR 0483954