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- W2043869968 abstract "The necessary form of a linearizable system of two second-order ordinary differential equations <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msubsup><mml:mi>y</mml:mi><mml:mn>1</mml:mn><mml:mo>″</mml:mo></mml:msubsup></mml:math><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>(<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>x</mml:mi></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msubsup><mml:mi>y</mml:mi><mml:mn>1</mml:mn><mml:mo>′</mml:mo></mml:msubsup></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msubsup><mml:mi>y</mml:mi><mml:mn>2</mml:mn><mml:mo>′</mml:mo></mml:msubsup></mml:math>), <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msubsup><mml:mi>y</mml:mi><mml:mn>2</mml:mn><mml:mo>″</mml:mo></mml:msubsup></mml:math><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>(<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>x</mml:mi></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msubsup><mml:mi>y</mml:mi><mml:mn>1</mml:mn><mml:mo>′</mml:mo></mml:msubsup></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msubsup><mml:mi>y</mml:mi><mml:mn>2</mml:mn><mml:mo>′</mml:mo></mml:msubsup></mml:math>) is obtained. Some other necessary conditions were also found. The main problem studied in the paper is to obtain criteria for a system to be equivalent to a linear system with constant coefficients under fiber preserving transformations. A linear system with constant coefficients is chosen because of its simplicity in finding the general solution. Examples demonstrating the procedure of using the linearization theorems are presented." @default.
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- W2043869968 date "2011-10-31" @default.
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- W2043869968 title "Linearization of Two Second-Order Ordinary Differential Equations via Fiber Preserving Point Transformations" @default.
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