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

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.