On linearization of third-order ordinary differential equations

A new algorithm for linearization of a third-order ordinary differential equation is presented. The algorithm consists of composition of two operations: reducing order of an ordinary differential equation and using the Lie linearization test for the obtained second-order ordinary differential equation. The application of the algorithm to several ordinary differential equations is given.

[1]  Sergey V. Meleshko,et al.  Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering , 2005 .

[2]  Nail H. Ibragimov,et al.  Linearization of third-order ordinary differential equations by point and contact transformations , 2005 .

[3]  Nail H. Ibragimov,et al.  Invariant Lagrangians and a new method of integration of nonlinear equations , 2005 .

[4]  Darryl D. Holm,et al.  Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves , 2003 .

[5]  N. Ibragimov.  Invariants of a Remarkable Family of Nonlinear Equations , 2002 .

[6]  Sylvain Neut,et al.  La géométrie de l'équation y = f ( x , y , y ′, y ″) , 2002 .

[7]  Thomas Wolf,et al.  Linearisable Third-Order Ordinary Differential Equations and Generalised Sundman Transformations: The Case X′′′=0 , 2002, nlin/0203028.

[8]  S. Gavrilyuk,et al.  Generalized vorticity for bubbly liquidand dispersive shallow water equations , 2001 .

[9]  V. N. Gusyatnikova,et al.  Contact Transformations and Local Reducibility of ODE to the Form y‴=0 , 1999 .

[10]  E. Cheb-Terrab,et al.  Integrating Factors for Second-order ODEs , 1999, Journal of symbolic computation.

[11]  P. Clarkson,et al.  Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations , 1999, math/9901154.

[12]  Guy Grebot,et al.  The Characterization of Third Order Ordinary Differential Equations Admitting a Transitive Fiber-Preserving Point Symmetry Group , 1997 .

[13]  P. Clarkson,et al.  Symmetries of a class of nonlinear third-order partial differential equations , 1996, solv-int/9609004.

[14]  L. M. Berkovich,et al.  The Method of an Exact Linearization of n-order Ordinary Differential Equations , 1996 .

[15]  L. G. S. Duarte,et al.  Linearization under nonpoint transformations , 1994 .

[16]  S. I. Svinolupov,et al.  ON SOME EQUIVALENCE PROBLEMS FOR DIFFERENTIAL EQUATIONS , 1993 .

[17]  L. M. Berkovich.  Method of exact linearization of nonlinear autonomous differential equations of second order , 1979 .