Symmetry classification of quasi-linear PDE's containing arbitrary functions

DOI10.1007/s11071-007-9212-7zbMath1179.35035arXivmath-ph/0702008OpenAlexW2070768820MaRDI QIDQ840380

Giampaolo Cicogna

Publication date: 11 September 2009

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0702008

zbMATH Keywords

determining equationsGrad-Schlüter-Shafranov equationgeneralized Laplace equation

Mathematics Subject Classification ID

Invariance and symmetry properties for PDEs on manifolds (58J70) Geometric theory, characteristics, transformations in context of PDEs (35A30) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items

Lie group analysis of a generalized Krichever-Novikov differential-difference equation ⋮ Group-invariant solutions for the Ricci curvature equation and the Einstein equation ⋮ Addendum to: Symmetry classification of quasi-linear PDE's. II: An exceptional case ⋮ Conformally invariant elliptic Liouville equation and its symmetry-preserving discretization ⋮ Differential invariants, hidden and conditional symmetry

Uses Software

• SYMMGRP
• SYMMGRP.MAX

Cites Work

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• Symmetries and conservation laws of Kadomtsev-Pogutse equations (Their computation and first applications)
• Group properties of a class of semilinear hyperbolic equations
• The computer calculation of Lie point symmetries of large systems of differential equations
• Review of symbolic software for Lie symmetry analysis
• General solutions to the 2D Liouville equation
• Liouville's formula under the viewpoint of minimal surfaces
• On the geometry of Liouville equation: symmetries, conservation laws, and Bäcklund transformations
• Symmetry and integration methods for differential equations
• Group classification of the general evolution equation: local and quasilocal symmetries
• Applications of symmetry methods to the theory of plasma physics
• New results on group classification of nonlinear diffusion–convection equations
• The symmetry and some exact solutions of the nonlinear many-dimensional Liouville, d'Alembert and eikonal equations
• Symmetry classification of KdV-type nonlinear evolution equations
• Symmetries and differential equations