Evolution of weak discontinuities in shallow water equations

DOI10.1016/J.AML.2009.10.003zbMath1182.35187OpenAlexW1987758880MaRDI QIDQ847321

T. Raja Sekhar, V. D. Sharma

Publication date: 12 February 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2009.10.003

zbMATH Keywords

exact solutionshallow water equationsgroup theoretic methodweak discontinuity

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (6)

Symmetry group analysis and exact solutions of isentropic magnetogasdynamics ⋮ Lie symmetries and exact solutions of shallow water equations with variable bottom ⋮ Exact solutions to magnetogasdynamics using Lie point symmetries ⋮ Similarity analysis of modified shallow water equations and evolution of weak waves ⋮ Application of Lie groups to compressible model of two-phase flows ⋮ Exact solutions to drift-flux multiphase flow models through Lie group symmetry analysis

Cites Work

• On the evolution law of weak discontinuities for hyperbolic quasi-linear systems
• Exact solutions to the unsteady equations of perfect gases through Lie group analysis and substitution principles
• On the evolution of weak discontinuities in a state characterized by invariant solutions
• The shallow water equations: explicit solutions and superposition principle
• On interaction of shock waves with weak discontinuities
• Uniformly valid analytical solution to the problem of a decaying shock wave
• The similarity solution for a bore on a beach
• Self-similar flows with uniform velocity gradient and their use in modelling the free expansion of polytropic gases
• Small amplitude gasdynamic disturbances in an exploding atmosphere
• When nonautonomous equations are equivalent to autonomopus ones
• Exact solutions to the ideal magneto-gas-dynamics equations through Lie group analysis and substitution principles
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries

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