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Research Article
Sachin Kumar
Central University of Punjab
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6883-7788
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This work is licensed under a CC BY 4.0 License. Read Full License
In this paper, the nonlinear transmission line model with the power law nonlinearity and the constant capacitance and voltage relationship is studied using Lie symmetry analysis. Corre- sponding to the infinitesimals obtained, using commutation relations, abelian and non abelian Lie subalgebras are obtained. Also, using the adjoint table, the one dimensional optimal system of subalgebra is presented. Based on the optimal system, corresponding Lie symmetry reduc- tions are obtained. Moreover, variety of new similarity solutions in the form of trigonometric functions, hyperbolic functions are obtained. Corresponding to one similarity reduction, by bifurcation of dynamical system, the stable and unstable regions are determined, which show the existence of soliton solutions from the nonlinear dynamics view point. Some of the obtained solutions are represented graphically and observations are also discussed.
Keywords
Nonlinear Transmission lines, Power law nonlinearity, Lie symmetry method, Exact Solutions, Bifurcation analysis
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CURRENT STATUS: Under Review
Version 1
Posted 16 Mar, 2021
No community comments so far
Editorial decision: Major revisions
On 28 Mar, 2021
Reviews received
Received 08 Mar, 2021
Reviewers invited
Invitations sent on 07 Mar, 2021
Editor assigned
On 05 Mar, 2021
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On 03 Mar, 2021
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Subject Areas
Mechanical Engineering
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This preprint is under consideration at Nonlinear Dynamics. A preprint is a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research Article
Sachin Kumar
Central University of Punjab
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6883-7788
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Under Review
Version 1
Posted 16 Mar, 2021
No community comments so far
Editorial decision: Major revisions
On 28 Mar, 2021
Reviews received
Received 08 Mar, 2021
Reviewers invited
Invitations sent on 07 Mar, 2021
Editor assigned
On 05 Mar, 2021
First submitted
On 03 Mar, 2021
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Mechanical Engineering
License:
This work is licensed under a CC BY 4.0 License. Read Full License
In this paper, the nonlinear transmission line model with the power law nonlinearity and the constant capacitance and voltage relationship is studied using Lie symmetry analysis. Corre- sponding to the infinitesimals obtained, using commutation relations, abelian and non abelian Lie subalgebras are obtained. Also, using the adjoint table, the one dimensional optimal system of subalgebra is presented. Based on the optimal system, corresponding Lie symmetry reduc- tions are obtained. Moreover, variety of new similarity solutions in the form of trigonometric functions, hyperbolic functions are obtained. Corresponding to one similarity reduction, by bifurcation of dynamical system, the stable and unstable regions are determined, which show the existence of soliton solutions from the nonlinear dynamics view point. Some of the obtained solutions are represented graphically and observations are also discussed.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
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