Symmetries of the shallow water equations in the Boussinesq approximation

DOI10.1016/J.CNSNS.2018.06.028zbMath1456.76030OpenAlexW2863748849WikidataQ129564843 ScholiaQ129564843MaRDI QIDQ2206077

Chompit Kaewmanee, Prakrong Voraka, Sergey V. Meleshko

Publication date: 21 October 2020

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.2018.06.028

zbMATH Keywords

Boussinesq approximationshallow water equationsLie groupNoether theoreminvariant solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Geometric theory, characteristics, transformations in context of PDEs (35A30) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60)

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One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: symmetry classification, conservation laws, difference schemes ⋮ Analysis of the one-dimensional Euler-Lagrange equation of continuum mechanics with a Lagrangian of a special form ⋮ Lie symmetry analysis, new group invariant for the \((3 + 1)\)-dimensional and variable coefficients for liquids with gas bubbles models ⋮ Lie group analysis and robust computational approach to examine mass transport process using Jeffrey fluid model

Cites Work

• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory
• Dissipative Boussinesq equations
• Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory
• Multi-symplectic, Lagrangian, one-dimensional gas dynamics
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