Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/linearisable-third-order-ordinary-differential-equations-and-0vSwOs30Tn
References (33)
-
P. Leach (1981)
An exact invariant for a class of time‐dependent anharmonic oscillators with cubic anharmonicityJournal of Mathematical Physics, 22
-
E. Kummer
De generali quadam aequatione differentiali tertii ordinis.Journal für die reine und angewandte Mathematik (Crelles Journal), 1887
-
M. Nucci, P. Leach (2000)
The harmony in the Kepler and related problemsJournal of Mathematical Physics, 42
-
T. Wolf (1996)
Relativity and Scientific Computing: Computer Algebra, Numerics, Visualization -
L. Hsu, N. Kamran (1989)
Classification of second-order ordinary differential equations admitting Lie groups of fibre-preserving point symmetriesProceedings of The London Mathematical Society, 58
-
L. Duarte, S. Duarte, I. Moreira (1987)
n-dimensional equations with the maximum number of symmetry generatorsJournal of Physics A, 22
-
W. Sarlet, F. Mahomed, P. Leach (1987)
Symmetries of nonlinear differential equations and linearisationJournal of Physics A, 20
-
H. Davis (1964)
Introduction to Nonlinear Differential and Integral Equations -
T. Wolf (1996)
The Program CRACK for Solving PDEs in General Relativity -
F. Mahomed, P. Leach (1990)
Symmetry Lie algebras of nth order ordinary differential equationsJournal of Mathematical Analysis and Applications, 151
-
(1967)
Lie Sophus -
A. Tresse
Determination des invariants ponctuels de l'equation differentielle ordinaire du second ordre y'' = w(x, y, y') -
(1887)
De generali quadam æquatione differentiali tertii ordinis J f¨ur Math 100 1-9 (reprinted from the Programm des evange-lischen K¨onigl und Stadtgymn in Liegnitz for the year 1834) -
V. N. Gusyatnikova, V. A. Yumaguzhin (1999)
Contact transformations and local reducibility of ordinary differential equation to the form y"' =0Acta Appl. Math., 56
-
(1988)
Normal forms for third order equations in Finite Dimensional Integrable Nonlinear Dynamical Systems Leach PGL -
S. Lie (1967)
Differentialgleichungen -
L. Berkovich (1996)
The Method of an Exact Linearization of n-order Ordinary Differential EquationsJournal of Nonlinear Mathematical Physics, 3
-
N. Euler (1997)
Transformation Properties ofJournal of Nonlinear Mathematical Physics, 4
-
K. Sundman (1913)
Mémoire sur le problème des trois corpsActa Mathematica, 36
-
N. Euler, M. Euler (2001)
A Tree of Linearisable Second-Order Evolution Equations by Generalised Hodograph TransformationsJournal of Nonlinear Mathematical Physics, 8
-
J. Liouville
Troisième mémoire sur le développement des fonctions ou parties de fonctions en séries dont les divers termes sont assujettis à satisfaire à une même équation différentielle du second ordre, contenant un paramètre variable.Journal de Mathématiques Pures et Appliquées
-
E. Kummer (1975)
De generali quadam aequatione differentiali tertii ordinis -
L. Duarte, I. Moreira, F. Santos (1994)
Linearization under nonpoint transformationsJournal of Physics A, 27
-
E. Laguerre (1898)
Oeuvres -
P. Leach, S. Cotsakis, G. Flessas (2000)
Symmetry, Singularities and Integrability in Complex Dynamics I: The Reduction ProblemJournal of Nonlinear Mathematical Physics, 7
-
G. Grebot (1997)
The Characterization of Third Order Ordinary Differential Equations Admitting a Transitive Fiber-Preserving Point Symmetry GroupJournal of Mathematical Analysis and Applications, 206
-
B. Abraham-Shrauner, P. Leach, K. Govinder, G. Ratcliff (1995)
HIDDEN AND CONTACT SYMMETRIES OF ORDINARY DIFFERENTIAL EQUATIONSJournal of Physics A, 28
-
Acta Applic Math -
C. Roberts, G. Belford (1971)
Stability and Entering of the Origin for Real, Nonlinear, Autonomous Differential Equations of Third OrderSiam Journal on Mathematical Analysis, 2
-
(1898)
Sur quelques invariants desdeséquations différentielles linéaires in: Oeuvres 1 Gauthiers-Villars -
V. Gusyatnikova, V. Yumaguzhin (1999)
Contact Transformations and Local Reducibility of ODE to the Form y‴=0Acta Applicandae Mathematica, 56
-
G. Reid, A. Wittkopf, A. Boulton (1996)
Reduction of systems of nonlinear partial differential equations to simplified involutive formsEuropean Journal of Applied Mathematics, 7
-
N. Euler (1997)
Transformation properties of x" + f 1 (t )x' + f 2 (t )x + f 3 (t )x pn =0J. Nonlinear Math. Phys., 4
- Publisher
- Springer Journals
- Copyright
- Copyright © 2003 by Kluwer Academic Publishers
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1023/A:1022838932176
- Publisher site
- See Article on Publisher Site
Abstract
We calculate in detail the conditions which allow the most general third-order ordinary differential equation to be linearised in X ′′′(T)=0 under the transformation X(T)=F(x,t), dT=G(x,t) dt.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 5, 2004