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Modulations of Sinh‐Gordon and Sine‐Gordon Wavetrains
Author(s) -
Forest M. Gregory,
McLaughlin David W.
Publication year - 1983
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/sapm198368111
Subject(s) - sine , sine gordon equation , eigenfunction , hyperbolic function , invariant (physics) , sine wave , mathematics , mathematical analysis , mathematical physics , representation (politics) , hamiltonian (control theory) , physics , soliton , nonlinear system , eigenvalues and eigenvectors , geometry , quantum mechanics , mathematical optimization , voltage , politics , political science , law
An invariant representation of the modulation equations for the sinh‐ and sine‐Gordon wavetrains is derived. A simple derivation of the representation which makes fundamental use of squared eigenfunctions is presented. This representation is used to place the modulation equations in Riemann invariant form and to cast them in a Hamiltonian form. The multiphase sinh‐Gordon study is complete, while the sine‐Gordon theory for more than one phase possesses technical difficulties which are described in the text. Explicit results on real two‐phase sine‐Gordon waves are included in Section VI.