Symmetry in Nonlinear Mathematical Physics - 2009
Asghar Qadir (National University of Sciences and Technology, Rawalpindi, Pakistan)
Conditional linearizability of higher order ordinary differential equations
Lie provided criteria for scalar, second order ordinary differential equations (ODEs)
to be convertible to linear form by
point transformations. This was extended by Neut and Petitot and by Ibragimov and
Meleshko to the third order and by Ibragimov and
Meleshko to the fourth order. Geometrical methods were used by Mahomed
and Qadir to provide criteria and methods to convert systems of
second order ODEs to linear form. In all these cases the number of linearly
independent solutions is equal to the order of the ODEs.
Mahomed and Qadir also developed a procedure to obtain solutions of third order
ODEs and systems of ODEs that may have only two
linearly independent solutions. This was called conditional linearizability.
Here this procedure is extended to higher orders.