The Soliton Theory
The adiabatic potential was discussed in the foregoing for pseudospin correlations in crystalline states. In this chapter, we learn that some aspects of the problem can be analyzed by the soliton theory in better accuracy. Mathematically, solutions of the Korteweg–deVries equation are expressed by elliptic functions of the propagating phase. The traditional concept of long-range order in crystalline states can be revised with soliton solutions, which however need to be subjected to phonon scatterings for thermodynamic descriptions. While collective pseudospins are not fully describable in one dimension, the soliton theory can explain the nonlinear propagation in sufficient accuracy.
KeywordsElliptic Function Spring Force Hypergeometric Equation Soliton Theory Adiabatic Potential
- 18.M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions. National Bureau of Standards Applied Mathematics Series, p. 253 (Government Printing Office, Washington, DC, 1964)Google Scholar