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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| Published in | Applied mathematics and computation Vol. 224; pp. 593 - 602 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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01.11.2013
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| Abstract | •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. |
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| AbstractList | •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. 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. |
| Author | Chandrasekar, V.K. Mohanasubha, R. Lakshmanan, M. Senthilvelan, M. Sheeba, Jane H. |
| Author_xml | – sequence: 1 givenname: R. surname: Mohanasubha fullname: Mohanasubha, R. – sequence: 2 givenname: Jane H. surname: Sheeba fullname: Sheeba, Jane H. – sequence: 3 givenname: V.K. surname: Chandrasekar fullname: Chandrasekar, V.K. – sequence: 4 givenname: M. surname: Senthilvelan fullname: Senthilvelan, M. email: velan@cnld.bdu.ac.in – sequence: 5 givenname: M. surname: Lakshmanan fullname: Lakshmanan, M. |
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| Cites_doi | 10.1103/PhysRevLett.18.510 10.1080/16073606.1989.9632170 10.1103/PhysRevE.72.066203 10.1088/0305-4470/39/31/006 10.1016/j.physleta.2012.04.058 10.1103/PhysRevLett.50.870 10.2991/jnmp.2004.11.3.9 10.1103/PhysRevA.41.4166 10.1143/JPSJ.44.1730 10.1007/BF02969405 10.1088/0305-4470/30/21/017 10.1063/1.526766 10.1098/rspa.2005.1465 10.1112/jlms/s1-36.1.33 10.1088/0034-4885/70/6/R03 10.1063/1.1664532 10.1111/1467-9590.00134 10.1098/rspa.2005.1648 10.1088/0305-4470/39/3/L01 10.1103/PhysRevA.30.2788 10.1088/0305-4470/26/19/030 10.1007/BF02393131 10.1063/1.2171520 10.1088/0951-7715/12/4/311 10.1080/16073606.1985.9631915 10.2991/jnmp.2002.9.3.4 10.1088/1751-8113/45/38/382002 |
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| Snippet | •We identified a class of integrable nonlinear complex ODEs.•Two types of nonlocal transformations which connect the nonlinear complex ODE with linear ODE are... In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce... |
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| SubjectTerms | Complex nonlinear oscillators Construction Differential equations Joints Linearization Mathematical analysis Mathematical models Nonlinearity Nonlocal transformation Oscillators Transformations |
| Title | A nonlocal connection between certain linear and nonlinear ordinary differential equations – Part II: Complex nonlinear oscillators |
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