Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation  

作　　者：Dahe Feng Jibin Li Airen Zhou Dahe Feng;Jibin Li;Airen Zhou(School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, China;School of Mathematical Sciences, Huaqiao University, Quanzhou, China)

机构地区：[1]School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, China [2]School of Mathematical Sciences, Huaqiao University, Quanzhou, China

出　　处：《Applied Mathematics》2024年第8期543-567,共25页应用数学（英文）

摘　　要：For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

关 键 词：(2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation BIFURCATIONS Phase Portrait Analytical Periodic Wave Solution Periodic Cusp Wave Solution 

分 类 号：O17[理学—数学]