# The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates

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*Robert J. Buckingham; Peter D. Miller*

#### Table of Contents

# Table of Contents

## The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates

- Chapter 1. Introduction 18 free
- 1.1. Pure impulse initial data for the sine-Gordon equation. Connection to the Zakharov-Shabat scattering problem 714 free
- 1.2. Exact solutions. Impulse threshold for generation of rotational waves 1017
- 1.3. Statement of results 1320
- 1.4. Outline of the rest of the Memoir 1926
- 1.5. Notation and terminology 2027

- Chapter 2. Formulation of the Inverse Problem for Fluxon Condensates 2330
- Chapter 3. Elementary Transformations of J(𝑤) 3138
- Chapter 4. Construction of 𝑔(𝑤) 4754
- Chapter 5. Use of 𝑔(𝑤) 8188
- Appendix A. Proofs of Propositions Concerning Initial Data 101108
- Appendix B. Details of the Outer Parametrix in Cases 𝖫 and 𝖱 105112
- Bibliography 135142