Abstract
This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.
Highlights
Physical applications of differential equations are in the form of nonlinear equations, which are very difficult to solve explicitly
He found the general form of all ordinary differential equations of second-order that can be reduced to a linear equation by changing the independent and dependent variables
In [7], linearization criteria for a system of two second-order ordinary differential equations to be equivalent to the linear system with constant coefficients matrix via fiber preserving point transformations were achieved
Summary
Physical applications of differential equations are in the form of nonlinear equations, which are very difficult to solve explicitly. He found the general form of all ordinary differential equations of second-order that can be reduced to a linear equation by changing the independent and dependent variables. Liouville [3] treated the equivalence problem for second-order ordinary differential equations in terms of relative invariants of the equivalence group of point transformations. In [7], linearization criteria for a system of two second-order ordinary differential equations to be equivalent to the linear system with constant coefficients matrix via fiber preserving point transformations were achieved. The linearization problem of a system of three second-order ordinary differential equations to be equivalent to linear system via point transformations is open.
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