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Generation of Secondary Solitary Waves in the Variable-Coefficient Korteweg-de Vries Equation

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posted on 2005-07-29, 15:49 authored by Roger Grimshaw, S.R. Pudjaprasetya
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.

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School

  • Science

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  • Mathematical Sciences

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97437 bytes

Publication date

2003

Notes

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.

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  • en

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