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Article
Periodic and Aperiodic Solitary Wave Solutions of the Nonlinear Klein-Gordon Equation without Dispersion
Journal of Physics A: Mathematical and General
  • Partha P. Banerjee, University of Dayton
  • G. Cao, Syracuse University
Document Type
Article
Publication Date
1-1-1988
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
Peer Reviewed
Yes
Citation Information
Partha P. Banerjee and G. Cao. "Periodic and Aperiodic Solitary Wave Solutions of the Nonlinear Klein-Gordon Equation without Dispersion" Journal of Physics A: Mathematical and General Vol. 21 Iss. 1 (1988)
Available at: http://works.bepress.com/partha_banerjee/91/