Mathematicians Buckingham (U. of Cincinnati) and Miller (U. of Michigan) examine the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and high-frequency librational motion in the tails. They find that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions, and that these formulae are consistent with predictions of Whitham's formal modulation theory in both the hyperbolic and elliptic cases. The treatise is not indexed. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)
Introduction Formulation of the inverse problem for fluxon condensates
Elementary transformations of $\mathbf{J}(w)$ Construction of $g(w)$ Use of
$g(w)$ Appendix A. Proofs of propositions concerning initial data Appendix B.
Details of the outer parametrix in cases $\mathsf{L}$ and $\mathsf{R}$
Bibliography
Robert J. Buckingham, University of Cincinnati, OH, USA
Peter D. Miller, University of Michigan, Ann Arbor, MI, USA
