Abstract
Linearization criteria for two-dimensional systems of second-order ordinary differential equations (ODEs) have been derived earlier using complex symmetry analysis. For such systems, the linearizable form, linearization criteria and symmetry group classification are presented. In this paper, we extend the complex approach to obtain a complex-linearizable form of two-dimensional systems of third-order ODEs. This form leads to a linearizable class and linearization criteria of these systems of ODEs.
Highlights
There are many methods available to solve differential equations analytically, except for some special cases of nonlinear ones that do not lend themselves to analytic solution
Linearizability of two-dimensional systems of second-order ordinary differential equations (ODEs) cannot be achieved by complex symmetry analysis (CSA) if the linearizing point transformations are more general than (11)
Complex linearization criteria are derived which led to linearization of a class of systems of third-order ODEs that can be linearized without the usual cumbersome calculations associated
Summary
There are many methods available to solve differential equations analytically, except for some special cases of nonlinear ones that do not lend themselves to analytic solution. Those special cases often rely on transformations of the dependent and independent variables so as to cast the nonlinear equations into linear forms. There is no classification available for linearizable systems of nth-order (n > 3) ODEs. As such, any progress towards canonically linearizing third-order systems is very useful, even if it is not a fully general canonical form of these systems of ODEs. In this paper, we present such a procedure for linearization of two-dimensional systems of third-order ODEs, based on complex methods for Lie symmetry analysis.
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