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Dmitrieva, V. V.

doi:10.1023/a:1010298623843

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2010

2023

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Cited by 3 publications

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Zeros of Solutions of Third-Order L–A Pairs and Linearizable Ordinary Differential Equations

Suleimanov

2023

Proc. Steklov Inst. Math.

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Zeros of Solutions of Third-Order L–A Pairs and Linearizable Ordinary Differential Equations

Suleimanov

2023

Proc. Steklov Inst. Math.

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A Systematic Method of Finding Linearizing Transformations for Nonlinear Ordinary Differential Equations I: Scalar Case

Chandrasekar¹,

Senthilvelan²,

Lakshmanan³

2012

JNMP

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In this paper we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of integrals of motion. The proposed algorithm is simple, straightforward and efficient and helps to unearth several new types of linearizing transformations besides the known ones in the literature. To make our studies systematic we divide our analysis into two parts. In the first part we confine our investigations to the scalar ODEs and in the second part we focus our attention on a system of two coupled second-order ODEs. In the case of scalar ODEs, we consider second and third-order nonlinear ODEs in detail and discuss the method of deriving maximal number of linearizing transformations irrespective of whether it is local or nonlocal type and illustrate the underlying theory with suitable examples. As a by-product of this investigation we unearth a new type of linearizing transformation in third-order nonlinear ODEs. Finally the study is extended to the case of general scalar ODEs. We then move on to the study of two coupled second-order nonlinear ODEs in the next part and show that the algorithm brings out a wide variety of linearization transformations. The extraction of maximal number of linearizing transformations in every case is illustrated with suitable examples.

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A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: I. Scalar case

Chandrasekar¹,

Senthilvelan²,

Lakshmanan³

2010

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Cited by 3 publications

References 11 publications

Zeros of Solutions of Third-Order L–A Pairs and Linearizable Ordinary Differential Equations

Zeros of Solutions of Third-Order L–A Pairs and Linearizable Ordinary Differential Equations

A Systematic Method of Finding Linearizing Transformations for Nonlinear Ordinary Differential Equations I: Scalar Case

A systematic method of finding linearizing transformations for nonlinear ordinary differential equations: I. Scalar case

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