Geodesic
Nonlinear long-wave models for imperfectly bonded layered waveguides
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 475-489

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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. 
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     author = {K. R. Khusnutdinova and A. M. Samsonov and A. S. Zakharov},
     title = {Nonlinear long-wave models for imperfectly bonded layered waveguides},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {475--489},
     publisher = {mathdoc},
     volume = {159},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a13/}
}
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K. R. Khusnutdinova; A. M. Samsonov; A. S. Zakharov. Nonlinear long-wave models for imperfectly bonded layered waveguides. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 475-489. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a13/