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Research Article
Yue-Sheng Wang
Beijing Jiaotong University
Corresponding Author
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In this paper, the governing equation in a pre-compressed one-dimensional granular crystal, which was previously discussed by Nesterenko [J. Appl. Mech. Phys. 24, 733 (1983)], is solved analytically. Multiple solitary wave solutions are obtained by using the homogeneous balance principle and Hirota’s bilinear method. We analyze the difference between the original system and the KdV system and examine the collision of solitary waves in some special parameters. The dynamic behavior and stability of the double solitary waves are also studied. We find that the opposite collision between single solitary waves may be stable and thus generate a stable double solitary wave. It is concluded that the collision is a special stable double solitary wave solution. We further propose a possible way to determine the stability of multiple solitary waves qualitatively.
Keywords
Nonlinear waves, Multiple solitary waves, Stability, Granular crystal
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CURRENT STATUS: Under Revision
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Posted 15 Mar, 2021
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Editorial decision: Major revisions
On 21 Mar, 2021
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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
Yue-Sheng Wang
Beijing Jiaotong University
Corresponding Author
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 Revision
Version 1
Posted 15 Mar, 2021
No community comments so far
Editorial decision: Major revisions
On 21 Mar, 2021
Reviewers invited
Invitations sent on 02 Mar, 2021
Review #? received
Received 02 Mar, 2021
Editor assigned
On 02 Mar, 2021
First submitted
On 01 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 governing equation in a pre-compressed one-dimensional granular crystal, which was previously discussed by Nesterenko [J. Appl. Mech. Phys. 24, 733 (1983)], is solved analytically. Multiple solitary wave solutions are obtained by using the homogeneous balance principle and Hirota’s bilinear method. We analyze the difference between the original system and the KdV system and examine the collision of solitary waves in some special parameters. The dynamic behavior and stability of the double solitary waves are also studied. We find that the opposite collision between single solitary waves may be stable and thus generate a stable double solitary wave. It is concluded that the collision is a special stable double solitary wave solution. We further propose a possible way to determine the stability of multiple solitary waves qualitatively.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 10
Figure 11
Figure 12
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