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Generation of Secondary Solitary Waves in the Variable-Coefficient Korteweg-de Vries Equation
preprint
posted on 2005-07-29, 15:49 authored by Roger Grimshaw, S.R. PudjaprasetyaWe consider the solitary wave solutions of a Korteweg-de Vries equation, where the
coefficients in the equation vary with time over a certain region. When these coefficients
vary rapidly compared with the solitary wave, then it is well-known that the solitary wave
may fission into two or more solitary waves. On the other hand, when these coefficients vary
slowly, the solitary wave deforms adiabatically with the production of a trailing shelf. In
this paper we re-examine this latter case, and show that the trailing shelf, on a very long
time-scale, can lead to the generation of small secondary solitary waves. This result thus
provides a connection between the adiabatic deformation regime, and the fission regime.
History
School
- Science
Department
- Mathematical Sciences
Pages
97437 bytesPublication date
2003Notes
This pre-print has been submitted, and accepted, to the journal, Studies in Applied Mathematics [© Blackwell]. The definitive version: GRIMSHAW, R.H.J. and PUDJAPRASETYA, S.R., 2004. Generation of Secondary Solitary Waves in the Variable-Coefficient Korteweg-de Vries Equation. Studies in Applied Mathematics, 112(3), pp. 271-279, is available at: http://www.blackwell-synergy.com/loi/sapm.Language
- en