Perturbative manifolds and the Noether generators of \(n\)th-order Poisson equations

DOI10.1016/j.jde.2018.09.025zbMath1410.76399OpenAlexW2893171875MaRDI QIDQ1710729

Sameerah Jamal

Publication date: 23 January 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.09.025

zbMATH Keywords

conservation lawPoisson equationpseudo-Riemannian manifoldNoether symmetryapproximate Lie symmetry

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hyperbolic conservation laws (35L65) Perturbations of PDEs on manifolds; asymptotics (58J37) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60)

Related Items

Approximate Lie symmetry conditions of autoparallels and geodesics ⋮ Unnamed Item ⋮ Singularity analysis and analytic solutions for the Benney-Gjevik equations ⋮ A study of the approximate singular Lagrangian-conditional Noether symmetries and first integrals

Cites Work

• Unnamed Item
• Comparison of approximate symmetry methods for differential equations
• Approximate symmetries and conservation laws of the geodesic equations for the Schwarzschild metric
• Group theoretic methods for approximate invariants and Lagrangians for some classes of \(y^{\prime\prime} + F(t)y^{\prime}+y=f(y,y^{\prime})\)
• Simplifying the form of Lie groups admitted by a given differential equation
• Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson equation
• \(n^{\text{th}}\)-order approximate Lagrangians induced by perturbative geometries
• A group theoretical application of \(\mathrm{SO}(4,1)\) in the de Sitter universe
• Approximate Noether symmetries
• Second-order approximate symmetries of the geodesic equations for the Reissner-Nordström metric and re-scaling of energy of a test particle
• Group invariant transformations for the Klein-Gordon equation in three dimensional flat spaces
• On approximate symmetry and approximate solutions of the nonlinear wave equation with a small parameter
• Approximate Lie symmetries of the Navier-Stokes equations
• APPROXIMATE SYMMETRIES
• On the construction of approximate solutions for a multidimensional nonlinear heat equation