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Investigation of Interaction Solutions for Modified Korteweg-de Vries Equation by Consistent Riccati Expansion Method

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  • Jin-Fu Liang
  • Xun Wang

Abstract

A consistent Riccati expansion (CRE) method is proposed for obtaining interaction solutions to the modified Korteweg-de Vries (mKdV) equation. Using the CRE method, it is shown that interaction solutions such as the soliton-tangent (or soliton-cotangent) wave cannot be constructed for the mKdV equation. More importantly, exact soliton-cnoidal periodic wave interaction solutions are presented. While soliton-cnoidal interaction solutions were found to degenerate to special resonant soliton solutions for the values of modulus ( n ) closer to one (upper bound of modulus) in the Jacobi elliptic function, a normal kink-shaped soliton was observed for values of n closer to zero (lower bound).

Suggested Citation

  • Jin-Fu Liang & Xun Wang, 2019. "Investigation of Interaction Solutions for Modified Korteweg-de Vries Equation by Consistent Riccati Expansion Method," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, July.
    • Handle: RePEc:hin:jnlmpe:9535294
    DOI: 10.1155/2019/9535294
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    Cited by:

    1. Abdel-Haleem Abdel-Aty & Mostafa M. A. Khater & Raghda A. M. Attia & Hichem Eleuch, 2020. "Exact Traveling and Nano-Solitons Wave Solitons of the Ionic Waves Propagating along Microtubules in Living Cells," Mathematics, MDPI, vol. 8(5), pages 1-11, May.

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