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Title: Generation of Secondary Solitary Waves in the Variable-Coefficient Korteweg-de Vries Equation
Authors: Grimshaw, Roger H.J.
Pudjaprasetya, S.R.
Issue Date: 2003
Abstract: We 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.
Description: 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.
URI: https://dspace.lboro.ac.uk/2134/302
Appears in Collections:Pre-prints (Maths)

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