Exact Solitary Wave Solutions of Nonlinear Evolution and Wave Equations using a Direct Algebraic Method

Author(s)

Willy Hereman, University of Iowa
Partha P. Banerjee, University of DaytonFollow
Adrianus Korpel, University of Iowa
Gaetano Assanto, Universitiá degli Studi di Palermo
A. Van Immerzeele, Instituut voor Theoretische Mechanica
A. Meerpoel, Instituut voor Theoretische Mechanica

Document Type

Article

Publication Date

1986

Publication Source

Journal of Physics A: Mathematical and General

Abstract

The authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations. The physical concept is one of the mixing of these elementary solutions through the nonlinearities in the system. The emphasis is, however, on the mathematical aspects, i.e. the formal procedure necessary to find single solitary wave solutions. By means of examples it is shown how various cases of pulse-type and kink-type solutions are to be obtained by this method. An exhaustive list of equations so treated is presented in tabular form, together with the particular intermediate relations necessary for deriving their solutions. The extension of the technique to construct N-soliton solutions and indicate connections with other existing methods is outlined.

Inclusive pages

607-628

ISBN/ISSN

0305-4470

Comments

Permission documentation is on file.

Copyright

Copyright © 1986, IOP Publishing

Publisher

IOP Publishing

Volume

19

Peer Reviewed

yes

Issue

5

eCommons Citation

Hereman, Willy; Banerjee, Partha P.; Korpel, Adrianus; Assanto, Gaetano; Van Immerzeele, A.; and Meerpoel, A., "Exact Solitary Wave Solutions of Nonlinear Evolution and Wave Equations using a Direct Algebraic Method" (1986). Electrical and Computer Engineering Faculty Publications. 211.
https://ecommons.udayton.edu/ece_fac_pub/211