Simulation of hyperbolic type solitary waves based on velocity parameter for (3 + 1)-dimensional the B-type Kadomtsev–Petviashvili–Boussinesq equation

In this paper, we investigate solutions to the [Formula: see text]-dimensional B-type Kadomtsev–Petviashvili–Boussinesq (B-KPB) equation, which has strong nonlinearity feature by using sub-equation and the modified [Formula: see text]-expansion methods. Using these analytical methods, dark soliton, trigonometric oscillation, singular soliton, algebraic and hyperbolic type oscillating traveling wave solutions are presented. By giving special values to the parameters in the obtained traveling wave solutions, 3D, 2D and contour graphs representing the solitary waves are drawn. The advantages and disadvantages of both analytical methods are presented in comparison with each other. In addition, the changes of the solutions of the B-KPB equation according to the velocity parameter and the refraction phenomenon are supported by simulation. In addition, the solutions of the equation discussed are first discussed in detail, physical interpretations. Secondly, the geometric interpretations of the traveling wave solutions are analyzed and it is shown that the graphs of the solutions correspond to flat hyper-surfaces. It is argued that these hyper-surfaces can be leveled on a hyperplane without distortion.