Soliton theory

Some difficulties of the soliton theory for explanation of the photovoltaic and other effects were also noted [124-127]. 

The nonlinear wave equation thus obtained is the famous sine-Gordon equation, which is well known from soliton theory (see, for example, Dodd et al. [1982] and Rajaraman [1982]). The long wave approximation used to replace the discrete rotor angle < by continuous variable 4>(x, t)... 

Nonlinear dispersion becomes relevant at sufficient pulse powers. In some fibre structures the interplay between the nonlinear dispersion and the group velocity dispersion can be used to produce non-dispersive waves called solitons. Solitons, although beyond the scope of this treatment, may revolutionize the communication systems of the future. A full treatment of soliton theory can be foimd in [4, 26]. 

Lamb G L Jr 1980 Elements of Soliton Theory (New York Wiley)... 

For the rest of this chapter we compare the above results with other ENDOR studies of polyacetylene. A spin density much more delocalized than that of the soliton theory was proposed from the studies of unoriented C-enriched cw-rich sample [110,116,117]. The proposed spin density consists of only two kinds of spin densities 0.06 and -0.02, the results being quite different from those obtained in stretched ci s-rich samples. The small magnitude of the proposed spin density of p(0) = 0.06 could result from the fact that the apparent frequency span of the C-enriched system, giving v o+ is much smaller than that of the pristine system. Proposed spin densities were deduced by the assignments of the structures of the observed lineshape to C or proton hyperfine components. Later comparison between pristine and C -enriched systems, however, revealed that the structures of the spectra of C-enriched system resulted from the... 

In order to understand the physical properties of polyacetylene doped with divalent ions, it is important to consider the theory of conductivity of polyacetylene doped with monovalent ions. One of the most unusual characteristics of polyacetylene is that small amounts of dopant ions give rise to enormous increases in electrical conductivity without causing any increase in the number of unpaired electrons. In fact, the small level of paramagnetism observed in pristine polyacetylene actually decreases on doping (8). This is in contrast to what occurs in traditional semiconductors, such as silicon, where dopants increase both conductivity and paramagnetism. An explanation has been offered by the soliton theory of conductivity (9,10). 

J.R. Taylor, Optical Solitons—Theory and Experiment (Cambridge Univ. Press, Cambridge,... 

Lamb, G.L., Jr., Elements of Soliton Theory, John Wiley Sons, New York, 1980. 

This topic will be addressed in the following section. The presented double-tracked strategy combines ab initio molecular dynamics studies of proton dynamics at highly acid-functionalized interfaces, with the development of a soliton theory. 

Long-Range Proton Transport at Interfaces Soliton Theory... 

A. Golovnev and M. Eikerhng, Soliton theory of interfacial proton transport in polymer... 

Double bonds can also be broken by excitation with light and thus solitons can be photogenerated. Photoexcitation is more likely to create charged solitons than neutral solitons and photoconductivity experiments might be a good way to test this concent. Several such experiments have been carried out(Fig.17).They show that photoconductivity is more pronounced in trans than in cis polyacetylene. In cis-polyacetylene solitons are unstable because of symmetry reasons (lattice forces will drive solitons to the chain ends (Fig. 25)) and so these experiments seem to support the soliton theory. 

One attractive aspect of the soliton theory of charge transport is that the carriers (cations or anions) carry no spin, i,e, the conducting compositions do not contain unpaired electrons, ESR experiments on the doping of PA(49) show that in certain intermediate doping regimes the spin concentration is much lower than expected from the observed conductivity values this phenomenon is referred to as spinless conductivity. If the conduction involved a normal process of defect-induced hole or electron transport, there would be a direct correlation between ESR determined spin concentration and conductivity. The same conclusion of spinless conduction is obtained from ESR experiments on doped PPP(61) however the soliton theory is not applicable to the PPP system(25). In Section VII, we present an alternate transport mechanism based on bipolarons (dications or dianions) which is applicable to all conducting polymer systems(26),... 

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