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

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  • Shek, E.C.M.
  • Chow, K.W.

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.

Suggested Citation

  • Shek, E.C.M. & Chow, K.W., 2008. "The discrete modified Korteweg–de Vries equation with non-vanishing boundary conditions: Interactions of solitons," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 296-302.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:2:p:296-302
    DOI: 10.1016/j.chaos.2006.06.036
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    References listed on IDEAS

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    1. Xie, Fuding & Wang, Jingquan, 2006. "A new method for solving nonlinear differential-difference equation," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1067-1071.
    2. Dai, Chaoqing & Zhang, Jiefang, 2006. "Jacobian elliptic function method for nonlinear differential-difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1042-1047.
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    1. Vakhnenko, Oleksiy O. & Vakhnenko, Vyacheslav O. & Verchenko, Andriy P., 2025. "Physical insight into the semi-discrete nonlinear integrable systems with the true and false multicomponentness," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).

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