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

Bo Ren

Advances in Mathematical Physics, 2021, vol. 2021, issue 1

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.

Date: 2021
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https://doi.org/10.1155/2021/6687632

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:6687632

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