Symmetry preserving parameterization schemes

DOI10.1063/1.4734344zbMath1277.58021arXiv1010.3010OpenAlexW3102358469MaRDI QIDQ2865530

Alexander Bihlo, Roman O. Popovych

Publication date: 29 November 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3010

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Invariance and symmetry properties for PDEs on manifolds (58J70) Applications of linear algebraic groups to the sciences (20G45)

Related Items (26)

Mapping method of group classification ⋮ Group classification of one-dimensional nonisentropic equations of fluids with internal inertia. II: General case ⋮ Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations ⋮ Lie reduction and exact solutions of vorticity equation on rotating sphere ⋮ Bäcklund transformation, infinitely-many conservation laws, solitary and periodic waves of an extended (3 + 1)-dimensional Jimbo–Miwa equation with time-dependent coefficients ⋮ Equivalence groupoid of a class of variable coefficient Korteweg–de Vries equations ⋮ Group analysis of general Burgers–Korteweg–de Vries equations ⋮ Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation ⋮ Enhanced group classification of gardner equations with time-dependent coefficients ⋮ Lie symmetries of two-dimensional shallow water equations with variable bottom topography ⋮ Invariant parameterization and turbulence modeling on the beta-plane ⋮ Extended symmetry analysis of an isothermal no-slip drift flux model ⋮ Inverse problem on conservation laws ⋮ Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations ⋮ Extended symmetry analysis of two-dimensional degenerate Burgers equation ⋮ Conservative parameterization schemes ⋮ Lie symmetries of generalized Burgers equations: application to boundary-value problems ⋮ Complete point symmetry group of the barotropic vorticity equation on a rotating sphere ⋮ Application of a Lie group admitted by a homogeneous equation for group classification of a corresponding inhomogeneous equation ⋮ Lie group classification for a class of compound KdV-Burgers equations with time-dependent coefficients ⋮ Application of group analysis to classification of systems of three second-order ordinary differential equations ⋮ Group classification of linear evolution equations ⋮ On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis ⋮ Complete group classification of systems of two linear second‐order ordinary differential equations: the algebraic approach ⋮ Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem ⋮ Complete group classification of a class of nonlinear wave equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Enhanced preliminary group classification of a class of generalized diffusion equations
• Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification
• More common errors in finding exact solutions of nonlinear differential equations. I
• A class of subgrid-scale models preserving the symmetry group of Navier--Stokes equations
• Analysis and development of subgrid turbulence models preserving the symmetry properties of the Navier-Stokes equations
• Generating differential invariants
• Algorithms for differential invariants of symmetry groups of differential equations
• Admissible transformations and normalized classes of nonlinear Schrödinger equations
• Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source
• Nonlocal symmetries. Heuristic approach
• Group classification of the equations of two-dimensional motions of a gas
• Moving coframes. I: A practical algorithm
• Applications of the differential invariants of infinite dimensional groups in hydrodynamics.
• Consequences of symmetries on the analysis and construction of turbulence models
• Group classification and exact solutions of nonlinear wave equations
• New results on group classification of nonlinear diffusion–convection equations
• Symmetry group analysis of the shallow water and semi-geostrophic equations
• Lie symmetries and exact solutions of the barotropic vorticity equation
• Preliminary group classification of equations v t t=f (x,v x)v x x+g(x,v x)
• A simple method for group analysis and its application to a model of detonation
• Group classification of heat conductivity equations with a nonlinear source
• Symmetry reduction and exact solutions of the Navier-Stokes equations. I
• Lie symmetry analysis and exact solutions of the quasigeostrophic two-layer problem
• A group analysis approach for a nonlinear differential system arising in diffusion phenomena
• The structure of Lie algebras and the classification problem for partial differential equations

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