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

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.

Families of exact solutions of a Generalized (2+1)-dimensional Boussinesq type equation

“…The Boussinesq equation was proposed by Boussinesq in 1871, which is used to describe the propagation of long waves in shallow water [26]. Today, many types of Boussinesq equations have been widely studied [27][28][29][30][31][32]. Among the (1+1)-dimensional equations, Boussinesq equation is one of the most studied equations due to its appearance in many physical systems [33,34].…”

Lump solution and interaction solutions to the fourth-order extended (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

“…Soliton equations can describe many nonlinear phenomena, for example, they play an important role in nonlinear mechanics, fluid optics, Marine science and other fields. So it is an important subject to study the nonlinear waves and exact solutions of soliton equations, such as Schödinger equation [1,2], Korteweg-de Vries equation [3,4], Boussinesq equation [5] and so on. With the deepening of the research, the development of nonlinear wave theory is promoted, especially in the Chen-Lee-Liu equation [6] and Manakov system [7][8][9][10], which show a lot of the latest progress of nonlinear wave theory.…”