A nonlocal connection between certain linear and nonlinear ordinary differential equations – Part II: Complex nonlinear oscillators

•We identified a class of integrable nonlinear complex ODEs.•Two types of nonlocal transformations which connect the nonlinear complex ODE with linear ODE are presented.•General solution of a class of nonlinear complex ODEs are given. In this paper, we present a method to identify integrable complex...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 224; pp. 593 - 602
Main Authors Mohanasubha, R., Sheeba, Jane H., Chandrasekar, V.K., Senthilvelan, M., Lakshmanan, M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2013
Subjects
Complex nonlinear oscillators
Construction
Differential equations
Joints
Linearization
Mathematical analysis
Mathematical models
Nonlinearity
Nonlocal transformation
Oscillators
Transformations
Complex nonlinear oscillators
Nonlocal transformation
Linearization
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Summary:•We identified a class of integrable nonlinear complex ODEs.•Two types of nonlocal transformations which connect the nonlinear complex ODE with linear ODE are presented.•General solution of a class of nonlinear complex ODEs are given. In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear complex ordinary differential equations (ODEs) with complex linear ODEs, thereby proving the integrability of the former. We also show how to construct the solutions using the two types of nonlocal transformations with several physically interesting cases as examples.
Bibliography:ObjectType-Article-2
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content type line 23
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.08.084