Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders

Details Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders

2009-02-02

arxiv.org/abs/0902.0275v1

Mathematics

Analysis of PDEs

39 pages, 17 figures

Scientific paper

Third-order nonlinear dispersion equations (NDEs) are shown to admit both
shock and rarefaction waves (as weak solutions), which are distinguished by a
smooth deformation approach. Compacton-type travelling wave solutions are
proved to be both delta-entropy and G-admissible (in the sense of I.M.
Gel'fand, 1963). Extensions to some higher-order NDEs are performed.

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