The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates
Author:   Robert J. Buckingham ,  Peter D. Miller
Publisher:   American Mathematical Society
Volume:   225, 1059
ISBN:  

9780821885451


Pages:   136
Publication Date:   01 September 2013
Format:   Paperback
Availability:   Temporarily unavailable   Availability explained
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The Sine-Gordon Equation in the Semiclassical Limit: Dynamics of Fluxon Condensates


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Overview

The authors study 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 also high-frequency 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.

Full Product Details

Author:   Robert J. Buckingham ,  Peter D. Miller
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   225, 1059
Weight:   0.226kg
ISBN:  

9780821885451


ISBN 10:   0821885456
Pages:   136
Publication Date:   01 September 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable   Availability explained
The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you.

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

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Robert J. Buckingham, University of Cincinnati, OH, USA Peter D. Miller, University of Michigan, Ann Arbor, MI, USA

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