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VARIATIONAL PRINCIPLE AND PERIODIC WAVE SOLUTIONALS FOR ELASTIC ROD EQUATION WITH FRACTAL DERIVATIVE.

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Title: VARIATIONAL PRINCIPLE AND PERIODIC WAVE SOLUTIONALS FOR ELASTIC ROD EQUATION WITH FRACTAL DERIVATIVE.
Authors: Yi TIAN1 ttxsun@163.com
Source: Thermal Science. 2025, Vol. 29 Issue 3B, p1871-1881. 11p.
Subjects: Variational principles, Conserved quantity, Elastic waves, Nonlinear waves, Equations
Abstract: The present research paper will demonstrate the variational principle and periodic wave solutions of the elastic rod equation. First, we will illustrate the generalized variational principle in two examples. Secondly, we consider a fractal non-linear elastic rod equation with an unsmooth boundary. Based on two-scale fractal theory and the semi-inverse method, we successfully establish the fractal variational principle for the non-linear elastic rod equation. This is helpful for studying symmetry, finding conserved quantities, and revealing possible traveling solution structures of the equation. Finally, we investigate periodic wave solutions of the non-linear elastic rod equation. [ABSTRACT FROM AUTHOR]
Copyright of Thermal Science is the property of Society of Thermal Engineers of Serbia and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: VARIATIONAL PRINCIPLE AND PERIODIC WAVE SOLUTIONALS FOR ELASTIC ROD EQUATION WITH FRACTAL DERIVATIVE.
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  Data: <searchLink fieldCode="AR" term="%22Yi+TIAN%22">Yi TIAN</searchLink><relatesTo>1</relatesTo><i> ttxsun@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Thermal+Science%22">Thermal Science</searchLink>. 2025, Vol. 29 Issue 3B, p1871-1881. 11p.
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  Label: Abstract
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  Data: The present research paper will demonstrate the variational principle and periodic wave solutions of the elastic rod equation. First, we will illustrate the generalized variational principle in two examples. Secondly, we consider a fractal non-linear elastic rod equation with an unsmooth boundary. Based on two-scale fractal theory and the semi-inverse method, we successfully establish the fractal variational principle for the non-linear elastic rod equation. This is helpful for studying symmetry, finding conserved quantities, and revealing possible traveling solution structures of the equation. Finally, we investigate periodic wave solutions of the non-linear elastic rod equation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Thermal Science is the property of Society of Thermal Engineers of Serbia and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.2298/TSCI2503871T
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 1871
    Subjects:
      – SubjectFull: Variational principles
        Type: general
      – SubjectFull: Conserved quantity
        Type: general
      – SubjectFull: Elastic waves
        Type: general
      – SubjectFull: Nonlinear waves
        Type: general
      – SubjectFull: Equations
        Type: general
    Titles:
      – TitleFull: VARIATIONAL PRINCIPLE AND PERIODIC WAVE SOLUTIONALS FOR ELASTIC ROD EQUATION WITH FRACTAL DERIVATIVE.
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            – D: 01
              M: 04
              Text: 2025
              Type: published
              Y: 2025
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            – TitleFull: Thermal Science
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