The Sine-Gordon Equation in the Semiclassical Limit (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
136
Utgivningsdatum
2013-09-30
Förlag
American Mathematical Society
Illustrationer
illustrations
ISSN
0065-9266
ISBN
9780821885451

The Sine-Gordon Equation in the Semiclassical Limit

Dynamics of Fluxon Condensates

av Robert J Buckingham, Peter D Miller
Häftad,  Engelska, 2013-09-30
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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.
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Övrig information

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

Innehållsförteckning

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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