The discrete modified Korteweg–de Vries equation with non-vanishing boundary conditions: Interactions of solitons

E.C.M. Shek and K.W. Chow

Chaos, Solitons & Fractals, 2008, vol. 36, issue 2, 296-302

Abstract: The discrete modified Korteweg–de Vries equation with negative cubic nonlinearity is considered for non-vanishing boundary condition in the far field. A Hirota bilinear form is established and expressions for 1- and 2-soliton are calculated. The amplitude of the soliton cannot exceed a maximum, and further increasing the wave number will just result in a solitary wave of larger width. This special class of solitary waves is termed ‘plateau’ solitons here. The interaction of a soliton of less than the maximum amplitude with such a ‘plateau’ soliton will result in a reversal of polarity of the smaller soliton during the interaction process.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:36:y:2008:i:2:p:296-302

DOI: 10.1016/j.chaos.2006.06.036

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