Abstract
We present a continuous family of kink-bearing potentials ${\mathit{V}}^{(\mathrm{\ensuremath{\Lambda}})}$(cphi) for a one-dimensional nonlinear Klein-Gordon equation. The form of these potentials has been reconstructed from the P\"oschl-Teller potential ${\mathit{U}}^{(\mathrm{\ensuremath{\Lambda}})}$(x), which has been assumed to describe the interaction between kinks and low-amplitude harmonic solutions (phonons). Shapes of kinks, their creation energy, the low-temperature free energy of a soliton gas, and other properties of the model are discussed. A physical interpretation of the characteristic parameter \ensuremath{\Lambda} (>0) of the investigated model is related to the total number of kink-phonon bound states and to their highest frequency. For special values of \ensuremath{\Lambda} the presented model can be reduced to the well-known sine-Gordon, ${\mathrm{\ensuremath{\varphi}}}^{4}$, Eshelby, double-quadratic, and, in part, to double-sine-Gordon models. Properties of kinks with three or four bound states are discussed in detail. We suggest that the model can be applied to quasi-one-dimensional solids.
Published Version
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