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5. Long-range interactions Interaction potentials discussed up to now allow a reduction in the continuum approximation to a SG-type equation with local interaction. , 1990). u ) dx. x) .

Of course, the continuum limit used above breaks down at P even in the case of gPR.  The predicted “rupture” of the atomic chain is a physical artifact which is explained by nonapplicability of the continuum limit approximation; such a “rupture” indicates only that the effective width of an antikink becomes smaller than the lattice spacing a , and the energy of disorder of a regular Q chain of antikinks is rather small. 3 below). , 1990). For ( the amplitude of the PN potential for the antikink tends to the value of the substrate  potential amplitude, "2 (see Fig.

1983). In a nonintegrable FK model, a breather may be excited in a result of inelastic (destructive) collision between a kink and antikink. In the sections which follow below, we consider several examples of the non-sinusoidal substrate potential » (u). [cos x#s cos(2x)] . 17) is topologically similar to the SG model for "s"(1/4, but it is characterized by flat bottoms for 1/4(s(0 or by sharp wells for 0(s(1/4. 1/4 and a double-barrier (DB) form for s'1/4. We would like to mention also more general on-site potentials proposed by Peyrard and Remoissenet (1982) (see also Remoissenet and Peyrard, 1984) which will be also analysed below.

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