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TMF, 2009, Volume 159, Number 3, Pages 475–489 (Mi tmf6366)  

This article is cited in 7 scientific papers (total in 7 papers)

Nonlinear long-wave models for imperfectly bonded layered waveguides

K. R. Khusnutdinovaa, A. M. Samsonovb, A. S. Zakharova

a Loughborough University
b Ioffe Physico-Technical Institute, Russian Academy of Sciences

Abstract: We propose a composite lattice model for describing nonlinear waves in a two-layer waveguide with adhesive bonding. We first consider waves in an anharmonic chain of oscillating dipoles and show that the corresponding asymptotic long-wave model for longitudinal waves coincides with the Boussinesq-type equation previously derived for a macroscopic waveguide using the nonlinear elasticity approach. We also show that in this model, there is no simple analogy between long longitudinal and long flexural waves. Then, for a composite lattice, we derive two new model systems of coupled Boussinesq-type equations for long nonlinear longitudinal waves and conjecture that a similar description exists in the framework of dynamic nonlinear elasticity.

Keywords: lattice model, long nonlinear wave, solitary wave

DOI: https://doi.org/10.4213/tmf6366

Full text: PDF file (640 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 159:3, 819–832

Bibliographic databases:


Citation: K. R. Khusnutdinova, A. M. Samsonov, A. S. Zakharov, “Nonlinear long-wave models for imperfectly bonded layered waveguides”, TMF, 159:3 (2009), 475–489; Theoret. and Math. Phys., 159:3 (2009), 819–832

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v159/i3/p475

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Khusnutdinova, KR, “Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures”, Physical Review E, 79:5 (2009), 056606  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    2. Popov I.Yu., Rodygina O.A., Chivilikhin S.A., Gusarov V.V., “Soliton in a nanotube wall and stokes flow in the nanotube”, Technical Physics Letters, 36:9 (2010), 852–855  crossref  adsnasa  isi  elib  scopus  scopus
    3. Popov I.Yu., Chivilikhin S.A., Gusarov V.V., “Model of fluid flow in nanotube: classical and quantum features”, International Conference on Theoretical Physics Dubna-Nano 2010, Journal of Physics Conference Series, 248, 2010  crossref  zmath  isi  scopus  scopus
    4. Belonenko M.B., Chivilikhin S.A., Gusarov V.V., Popov I.Yu., Rodygina O.A., “Soliton-Induced Flow in Carbon Nanotubes”, EPL, 101:6 (2013), 66001  crossref  adsnasa  isi  elib  scopus  scopus
    5. A. I. Zemlyanukhin, A. V. Bochkarev, “Steady solitary wave solutions of the generalized sixth-order Boussinesq–Ostrovsky equation”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:3 (2015), 338–347  mathnet  elib
    6. Bochkarev A.V., Zemlyanukhin A.I., Mogilevich L.I., “Solitary Waves in An Inhomogeneous Cylindrical Shell Interacting With An Elastic Medium”, Acoust. Phys., 63:2 (2017), 148–153  crossref  isi  scopus
    7. Chivilikhin S.A., Gusarov V.V., Popov I.Yu., “Charge Pumping in Nanotube Filled With Electrolyte”, Chin. J. Phys., 56:5 (2018), 2531–2537  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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