Symmetry group classification of ordinary differential equations: Survey of some results
From MaRDI portal
Publication:5437554
DOI10.1002/mma.934zbMath1135.34029OpenAlexW2092649809MaRDI QIDQ5437554
Publication date: 21 January 2008
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mma.934
Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Linear ordinary differential equations and systems (34A30) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)
Related Items
Axisymmetric spreading of a thin power-law fluid under gravity on a horizontal plane, Reduction of systems of two nonlinear parabolic type partial differential equations to solvable forms using differential invariants, Submaximal metric projective and metric affine structures, A group theoretical identification of integrable cases of the Liénard-type equation ẍ+f(x)ẋ+g(x)=. I. Equations having nonmaximal number of Lie point symmetries, Lie point symmetries classification of the mixed Liénard-type equation, Group classification for path equation describing minimum drag work and symmetry reductions, Linearizing systems of second-order ODEs via symmetry generators spanning a simple subalgebra, Lie symmetries and similarity solutions for a family of 1+1 fifth-order partial differential equations, Symmetry Solutions of a Third-Order Ordinary Differential Equation which Arises from Prandtl Boundary Layer Equations, Steady heat transfer through a radial fin with rectangular and hyperbolic profiles, Conditional symmetries of nonlinear third-order ordinary differential equations, Linearizability of systems of ordinary differential equations obtained by complex symmetry analysis, Classical Lie point symmetry analysis of a steady nonlinear one-dimensional fin problem, Some remarks on the solution of linearisable second-order ordinary differential equations via point transformations, Unnamed Item, Linearizabiliy and Lax representations for cubic autonomous and non-autonomous nonlinear oscillators, One-dimensional optimal system and similarity transformations for the \(3+1\) Kudryashov-Sinelshchikov equation, Application of the \(\lambda\)-symmetries approach and time independent integral of the modified Emden equation, Steady one-dimensional heat flow in a longitudinal triangular and parabolic fin, Linearizability criteria for systems of two second-order differential equations by complex methods, Algebraic properties of first integrals for scalar linear third-order ODEs of maximal symmetry, Algebraic linearization criteria for systems of ordinary differential equations, Invariant characterization of third-order ordinary differential equations \(u'= f(x, u, u', u)\) with five-dimensional point symmetry group, Lie and Riccati linearization of a class of Liénard type equations, Linearization: geometric, complex, and conditional, Symmetry classification of first integrals for scalar linearizable second-order ODEs, Lie point symmetries, partial Noether operators and first integrals of the Painlevé-Gambier equations, Exact solutions of the \((2+1)\)-dimensional Zakharov-Kuznetsov modified equal width equation using Lie group analysis, Comparison of exact solutions for heat transfer in extended surfaces of different geometries, Invariant solutions and conservation laws of the (2 + 1)-dimensional Boussinesq equation, Comparison of different approaches to construct first integrals for ordinary differential equations, Optimal system and classification of invariant solutions of nonlinear class of wave equations and their conservation laws, Classification of Lie point symmetries for quadratic Liénard type equation $\ddot{x}+f(x)\dot{x}^2+g(x)=0$ẍ+f(x)ẋ2+g(x)=0, A note on the integrability of a remarkable static Euler-Bernoulli beam equation, A group theoretical identification of integrable equations in the Liénard-type equation ẍ+f(x)ẋ+g(x)=. II. Equations having maximal Lie point symmetries, Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One, Group classification of differential-difference equations: low-dimensional Lie algebras, Algorithmic symmetry classification with invariance, Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity, Symmetry analysis for the nonlinear model of diffusion and reaction in porous catalysts, Two-dimensional systems that arise from the Noether classification of Lagrangians on the line, A Lie symmetry approach to nonlinear Schrödinger's equation with non-Kerr law nonlinearity, Invariants of third-order ordinary differential equationsy′′′=f(x,y,y′,y′′) via point transformations, Symmetry analysis of a heat conduction model for heat transfer in a longitudinal rectangular fin of a heterogeneous material, An alternative proof of Lie's linearization theorem using a new \(\lambda\)-symmetry criterion, Reduction of fourth order ordinary differential equations to second and third order Lie linearizable forms, Thin film flow of non-Newtonian MHD fluid on a vertically moving belt, Lie group classification of the generalized Lane-Emden equation, Third-order ordinary differential equationsy′′′ =f(x, y, y′, y″)with maximal symmetry group, Classification of scalar third order ordinary differential equations linearizable via generalized contact transformations, Invariant Linearization Criteria for Systems of Cubically Nonlinear Second-Order Ordinary Differential Equations, Comparison of symmetry and homotopy solutions for nonlinear heat transfer systems, Symmetry analysis of space-time fractional Poisson equation with a delay, Linearization criteria for two-dimensional systems of third-order ordinary differential equations by complex approach, Symmetry analysis of the Klein–Gordon equation in Bianchi I spacetimes, Symmetries and integrability of a fourth-order Euler–Bernoulli beam equation, Symmetry and transformation properties of iterative ordinary differential equation, Symmetry analysis for a fourth-order noise-reduction partial differential equation
Cites Work
- Unnamed Item
- Unnamed Item
- The characterization of third order ordinary differential equations admitting a transitive fiber-preserving point symmetry group
- The geometry of the equation \(y'=f(x,y,y',y)\)
- Symmetry properties of autonomous integrating factors
- The complete symmetry group of a forced harmonic oscillator
- Applications of the Lie theory of extended groups in Hamiltonian mechanics: the oscillator and the Kepler problem
- Symmetry algebras of third-order ordinary differential equations
