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Modulational Stability of Two‐Phase Sine‐Gordon Wavetrains
Author(s) -
Ercolani Nicholas,
Forest M. Gregory,
McLaughlin David W.
Publication year - 1984
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198471291
Subject(s) - integrable system , sine , breather , modulational instability , sine gordon equation , invariant (physics) , soliton , mathematical physics , korteweg–de vries equation , physics , mathematical analysis , modulation (music) , sine wave , phase (matter) , mathematics , nonlinear system , quantum mechanics , geometry , acoustics , voltage
A modulational stability analysis is presented for real, two‐phase sine‐Gordon wavetrains. Using recent results on the geometry of these real solutions, an invariant representation in terms of Abelian differentials is derived for the sine‐Gordon modulation equations. The theory thus attains the same integrable features of the previously completed KdV and sinh‐Gordon modulations. The twophase results are as follows: kink‐kink trains are stable, while the breather trains and kink‐radiation trains are unstable, to modulations.