Fermi resonance interface waves

Now we shall consider the case when one interface separates two simple cubic 2D crystals composed of different molecules of types a and b interacting across the interface. In two dimensions with a linear interface (the 3D generalization is straightforward) the equations of motion for the amplitudes Amn and Bmn read (compare with eqn 9.40) 

These equations give the values of na and k , as functions of K and fl. Then eqns (9.46) reduce to 

Elimination of VacK 1 and V),eKb from this equation can be done with the use of eqn (9.48), and yields the relation defining implicitly the dependence of Q on K, i.e. the dispersion laws of Fermi resonance modes 

We see that they are modified compared to the case of Fermi resonance waves (9.44), (9.45) in an infinite ID cubic crystal. At / = 0 (or T = 0), when the 

Note that the addition of a new dimension to a ID cubic crystal with point interface leads to the replacements 

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