An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics

DOI10.1063/1.2956502zbMath1152.81374OpenAlexW2017657016MaRDI QIDQ5505020

Alexei F. Cheviakov

Publication date: 23 January 2009

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

Full work available at URL: https://doi.org/10.1063/1.2956502

Mathematics Subject Classification ID

Gas dynamics (general theory) (76N15) Geometric theory, characteristics, transformations in context of PDEs (35A30) Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60)

Related Items (6)

Nonlocal symmetries classifications and exact solution of Chaplygin gas equations ⋮ Application of symmetry analysis to viscoelastic fluid model ⋮ A symmetry-based method for constructing nonlocally related partial differential equation systems ⋮ Similarity: Generalizations, applications and open problems ⋮ On locally and nonlocally related potential systems ⋮ Multi-symplectic, Lagrangian, one-dimensional gas dynamics

Cites Work

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• Local and nonlocal symmetries for nonlinear telegraph equation
• Hierarchy of conservation laws of diffusion-convection equations
• Framework for potential systems and nonlocal symmetries: Algorithmic approach
• Framework for nonlocally related partial differential equation systems and nonlocal symmetries: Extension, simplification, and examples
• Nonlocal symmetries and nonlocal conservation laws of Maxwell’s equations
• Direct Construction of Conservation Laws from Field Equations
• A comparison of four approaches to the calculation of conservation laws
• Potential symmetries and solutions by reduction of partial differential equations
• Infinite symmetries of the ideal MHD equilibrium equations

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