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Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation

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  • Bo Ren

Abstract

The Painlevé integrability of the higher-order Boussinesq equation is proved by using the standard Weiss-Tabor-Carnevale (WTC) method. The multisoliton solutions of the higher-order Boussinesq equation are obtained by introducing dependent variable transformation. The soliton molecule and asymmetric soliton of the higher-order Boussinesq equation can be constructed by the velocity resonance mechanism. Lump solution can be derived by solving the bilinear form of the higher-order Boussinesq equation. By some detailed calculations, the lump wave of the higher-order Boussinesq equation is just the bright form. These types of the localized excitations are exhibited by selecting suitable parameters.

Suggested Citation

  • Bo Ren, 2021. "Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-6, February.
    • Handle: RePEc:hin:jnlamp:6687632
    DOI: 10.1155/2021/6687632
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