Open AccessPainlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation
Author(s) -
Bo Ren
Publication year - 2021
Publication title -
advances in mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.283
H-Index - 23
eISSN - 1687-9139
pISSN - 1687-9120
DOI - 10.1155/2021/6687632
Subject(s) - soliton , boussinesq approximation (buoyancy) , bilinear interpolation , transformation (genetics) , bilinear form , mathematics , order (exchange) , mathematical analysis , scheme (mathematics) , sine gordon equation , physics , nonlinear system , mechanics , quantum mechanics , chemistry , biochemistry , statistics , natural convection , finance , rayleigh number , economics , gene , convection
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.