MODULATIONS OF SINH-GORDON AND SINE-GORDON WAVETRAINS.

M. Gregory Forest; David W. McLaughlin

doi:10.1002/sapm198368111

MODULATIONS OF SINH-GORDON AND SINE-GORDON WAVETRAINS.

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Abstract

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.

Original language	English (US)
Pages (from-to)	11-59
Number of pages	49
Journal	Studies in Applied Mathematics
Volume	68
Issue number	1
DOIs	https://doi.org/10.1002/sapm198368111
State	Published - 1983

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Applied Mathematics

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abstract = "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.",

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AB - 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.

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MODULATIONS OF SINH-GORDON AND SINE-GORDON WAVETRAINS.

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