Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
P. M. Morse and H. Feshbach, Methods of Theoretical Physics, p. 1651 (McGraw-Hill, New York, 1953)
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)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Fujimoto, M. (2010). The Soliton Theory. In: Thermodynamics of Crystalline States. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6688-9_8
Download citation
DOI: https://doi.org/10.1007/978-1-4419-6688-9_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-6687-2
Online ISBN: 978-1-4419-6688-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)