Davydov’s Soliton Revisited: Self-Trapping of Vibrational by A. S. Davydov (auth.), Peter Leth Christiansen, Alwyn C.

By A. S. Davydov (auth.), Peter Leth Christiansen, Alwyn C. Scott (eds.)

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15eV. 05eV, the quasi-particle effective mass in the conductivity band is about ~ 102m. So the nonlinear bisoliton model, based on strong electron-phonon coupling, allows one to explain the following peculiarities of ceramic high-temperature superconductors: 1. The small correlation radius of paired quasi-particles. 2. The very small isotopic effect. 3. Nonmonotone dependence of temperature of the transition to a superconductivity that vanishes at very large and very small concentrations. 4. The different energy gap width values ~ obtained in tunneling studies and in infrared spectroscopy methods.

Respectively. We close this section by giving a br1ef remark on the difference and the similarity existing for the dispersion relation of anharmonic localized modes in the NKG equation and the NLS equation. We note that Eq. 10). This shows that in the stationary regime the anharmonic localized mode of the NKG equation is similar to that of 37 the NLS equation. For moving anharmonic localized mode the dispersion relation for the NKG equation has a form different from that for the NLS equation.

6) is the dispersion relation for the soliton. l), where A and Sn are identified as the amplitude of the localized mode and its shape function, respectively. 1) is a slightly modified version of the Ablowitz-Ladik equation. 7) n to show that it yields exact solitons. l) from the viewpoint of the dynamical self-trapping. A more physical insight into the nature of solitons here can be gained by rewriting the dispersion relation in terms of ~ and A as W = tV 0 - 2Jcos(ka) [ 1 + (i\ /J)A 2 1/2 1 . 8) This is to be compared with the dispersion relation i,I IV 2 2 = W 0 - 2J + Ja k - l\.

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