Memoirs of the American Mathematical Society 2013; 136 pp; softcover Volume: 225 ISBN10: 0821885456 ISBN13: 9780821885451 List Price: US$74 Individual Members: US$44.40 Institutional Members: US$59.20 Order Code: MEMO/225/1059
 The authors study the Cauchy problem for the sineGordon equation in the semiclassical limit with pureimpulse initial data of sufficient strength to generate both highfrequency rotational motion near the peak of the impulse profile and also highfrequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases. Table of Contents  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
