Similarity analysis of modified shallow water equations and evolution of weak waves

DOI10.1016/j.cnsns.2011.06.011zbMath1245.35097OpenAlexW2084400940MaRDI QIDQ430329

T. Raja Sekhar, V. D. Sharma

Publication date: 21 June 2012

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2011.06.011

zbMATH Keywords

exact solutiongroup theoretic methodmodified shallow water equationsweak discontinuity

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Methods of ordinary differential equations applied to PDEs (35A24) Second-order quasilinear hyperbolic equations (35L72)

Related Items (11)

Evolution of contact and weak discontinuity waves in two phase drift flux model ⋮ On group-invariant solutions of Konopelchenko-Dubrovsky equation by using Lie symmetry approach ⋮ Exact solutions to magnetogasdynamics using Lie point symmetries ⋮ Solitary wave solutions of mKdV–Calogero–Bogoyavlenskii–Schiff equation by using Lie symmetry analysis ⋮ On Lie symmetries and invariant solutions of (2+1)-dimensional Gardner equation ⋮ NUMERICAL STUDY OF MIXED CONVECTION FLOW OF A MICROPOLAR FLUID TOWARDS PERMEABLE VERTICAL PLATE WITH CONVECTIVE BOUNDARY CONDITION ⋮ Analysis of the one-dimensional Euler-Lagrange equation of continuum mechanics with a Lagrangian of a special form ⋮ Similarity solutions of the Konopelchenko-Dubrovsky system using Lie group theory ⋮ Some group-invariant solutions of potential Kadomtsev-Petviashvili equation by using Lie symmetry approach ⋮ Symmetry analysis of a system of modified shallow-water equations ⋮ Evolution of weak discontinuities in non-ideal magnetogasdynamic equations

Cites Work

• Unnamed Item
• Unnamed Item
• On the evolution law of weak discontinuities for hyperbolic quasi-linear systems
• Evolution of weak discontinuities in shallow water equations
• Self-similar shocks in a dusty gas
• Similarity solutions of the Euler equation and the Navier-Stokes equation in two space dimensions
• Similarity solutions for converging shocks in a relaxing gas
• Similarity solutions for three-dimensional Euler equations using Lie group analysis
• On interaction of shock waves with weak discontinuities
• Interaction of Shallow Water Waves
• Uniformly valid analytical solution to the problem of a decaying shock wave
• Self-similar flows with uniform velocity gradient and their use in modelling the free expansion of polytropic gases
• Similarity Solutions for Reactive Shock Hydrodynamics
• Small amplitude gasdynamic disturbances in an exploding atmosphere
• When nonautonomous equations are equivalent to autonomopus ones
• Particular solutions and Riemann problem for modified shallow water equations
• Exact solutions to the ideal magneto-gas-dynamics equations through Lie group analysis and substitution principles
• Nonlinear boundary value problems in science and engineering
• Symmetries and differential equations

This page was built for publication: Similarity analysis of modified shallow water equations and evolution of weak waves