headerpos: 12198
 
 
 

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
Publisher
Journal Information
» Editorial Board
» Editorial Policy
» Archival Policy
» Article Publication Charges
» Copyright and Licensing Policy
Guidelines for Authors
» For Authors
» Instructions to Authors
» LaTex style files
Guidelines for Reviewers
» For Reviewers
» Review Form
Open Access
List of Issues
» 2019
» 2018
» 2017
» 2016
» 2015
» 2014
» 2013
» 2012
» 2011
» 2010
Vol. 59, Issue 4
Vol. 59, Issue 3
Vol. 59, Issue 2
Vol. 59, Issue 1
» 2009
» 2008
» Back Issues Phys. Math.
» Back Issues Chemistry
» Back issues (full texts)
  in Google. Phys. Math.
» Back issues (full texts)
  in Google. Chemistry
» Back issues (full texts)
  in Google Engineering
» Back issues (full texts)
  in Google Ecology
» Back issues in ETERA Füüsika, Matemaatika jt
Subscription Information
» Prices
Internet Links
Support & Contact
Publisher
» Staff
» Other journals

On periodic waves governed by the extended Korteweg–de Vries equation; pp. 133–138

(Full article in PDF format) doi: 10.3176/proc.2010.2.11


Authors

Manfred Braun, Merle Randrüüt

Abstract

The evolution equation describing the propagation of one-dimensional waves in a microstructured material has the form of an extended Korteweg–de Vries equation, where the additional term reflects the influence of micrononlinearity. As shown by Janno and Engelbrecht (J. Phys. A: Math. Gen., 2005, 38, 5159–5172), solitary waves in a microstructured material become asymmetric if nonlinearities are taken into account in both macro- and microscale. The present paper generalizes previous results to periodic waves which, in the KdV case, have the form of cnoidal waves. It is shown that, due to the nonlinearity in microscale, these waves become inclined in the same manner as solitary waves, while the relations between the period, amplitude, and velocity are not affected.

Keywords

materials with microstructure, cnoidal waves, solitary waves, KdV equation.

References

1. Mindlin , R. D. Microstructure in linear elasticity. Arch. Rat. Mech. Analysis , 1964 , 16 , 51–78.
doi:10.1007/BF00248490

2. Engelbrecht , J. and Pastrone , F. Waves in microstructured solids with strong nonlinearities in microscale. Proc. Estonian Acad. Sci. Phys. Math. , 2003 , 52 , 12–20.

3. Janno , J. and Engelbrecht , J. Solitary waves in nonlinear microstructured materials. J. Phys. A: Math. Gen. , 2005 , 38 , 5159–5172.
doi:10.1088/0305-4470/38/23/006

4. Randrüüt , M. and Braun , M. On one-dimensional solitary waves in microstructured solids. Wave Motion , 2010 , 47 , 217–230.
doi:10.1016/j.wavemoti.2009.11.002

5. Randrüüt , M. , Salupere , A. , and Engelbrecht , J. On modelling wave motion in microstructured solids. Proc. Estonian Acad. Sci. Phys. Math. , 2009 , 58 , 241–246.
doi:10.3176/proc.2009.4.05
 
Back

Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December