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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
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Transverse instability of nonlinear longitudinal waves in hexagonal lattices; pp. 349–355

(Full article in PDF format) doi: 10.3176/proc.2015.3S.04


Authors

Alexey Porubov, Igor Andrianov, Berndt Markert

Abstract

Various continuum limits of the original discrete hexagonal lattice model are used to obtain transverse weakly nonlinear equations for longitudinal waves. It is shown, that the long wavelength continuum limit gives rise to the Kadomtsev–Petviashvili equation, while another continuum limit results in obtaining two-dimensional generalization of the nonlinear Schrödinger equation.

Keywords

nonlinear hexagonal lattice, continuum limit, nonlinear differential equation, asymptotic solution.

References

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http://dx.doi.org/10.1016/0021-9991(67)90031-9

  4. Porubov , A. V. and Berinskii , I. E. Non-linear plane waves in materials having hexagonal internal structure. Int. J. Non-Linear Mech. , 2014 , 67 , 27–33.
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  8. Porubov , A. V. , Tsuji , H. , Lavrenov , I. V. , and Oikawa , M. Formation of the rogue wave due to nonlinear two-dimensional waves interaction. Wave Motion , 2005 , 42 , 202–210.
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12. Porubov , A. V. , Aero , E. L. , and Maugin , G. A. Two approaches to study essentially nonlinear and dispersive properties of the internal structure of materials. Phys. Rev. E , 2009 , 79 , 046608.
http://dx.doi.org/10.1103/PhysRevE.79.046608

 
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Current Issue: Vol. 68, Issue 3, 2019




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