The Sine-Gordon Equation in the Semiclassical Limit 1

Vetenskap & teknik

The Sine-Gordon Equation in the Semiclassical Limit

Robert J Buckingham • Peter D Miller

Pocket

1439:-

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136 sidor
2013

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.

Författare: Robert J Buckingham, Peter D Miller
Format: Pocket/Paperback
ISBN: 9780821885451
Språk: Engelska
Antal sidor: 136
Utgivningsdatum: 2013-09-30
Förlag: American Mathematical Society