Title

Periodic and Aperiodic Solitary Wave Solutions of the Nonlinear Klein-Gordon Equation without Dispersion

Document Type

Article

Publication Date

1988

Publication Source

Journal of Physics A: Mathematical and General

Abstract

The Klein-Gordon equation without dispersion, and with quadratic and cubic nonlinearities, has been studied in one and higher dimensions. Algebraic solitary wave solutions in all cases, as well as higher-order modes in higher dimensions (similar to nonlinear optics) have been shown to exist corresponding to specific initial values. While in the one-dimensional case, arbitrary initial values yield periodic solutions, asymptotically stable solutions are shown to exist in the higher-dimensional case. For both one- and higher-dimensional cases, solutions tending to zero with distance are shown to be achieved for other initial conditions by incorporating a small amount of 'saturating' fourth-order nonlinearity. Finally, it is shown how a general Klein-Gordon equation with dispersion and a forcing term may be reduced to the equation discussed in the paper.

Inclusive pages

55-71

ISBN/ISSN

0305-4470

Comments

Permission documentation is on file.

Publisher

IOP Publishing

Volume

21

Issue

1

Peer Reviewed

yes