Multiple soliton and lump solutions to a variety of novel integrable multi-dimensional Boussinesq-type equations

Abstract

Several scientific fields, including mechanical fluids, plasmas, and solids, use higher-dimensional Boussinesq-type equations to model various nonlinear phenomena, such as solitary and shock waves, as well as lump waves. Motivated by these applications, this investigation focuses on studying and analyzing four novel integrable higher-dimensional Boussinesq and Boussinesq-type equations, drawing from the many and varied applications of this family of evolution equations. To the best of the author’s knowledge, these four models are constructed and introduced for the first time. We first check the complete integrability for the four suggested models via Painlevé analysis. Next, we employ the simplified Hirota’s method (SHM) to solve the four proposed models and derive multiple soliton solutions. Our results show that the simplified Hirota’s approach is efficient and robust for solving these equations. In addition, we use symbolic computation with Maple to explicitly derive two distinct categories of lump solutions for each equation. We numerically investigate all derived solitary and lump solutions to understand the dynamical behavior of these waves. Note that this approach can also derive other lump solutions. This study’s findings should benefit many researchers in fluid and plasma physics and analytical engineering should benefit from the findings of this study.