Diverse Soliton wave solutions of for the nonlinear potential Kadomtsev–Petviashvili and Calogero–Degasperis equations

Abstract

This paper investigates the soliton wave structures of the nonlinear potential Kadomtsev–Petviashvili and Calogero–Degasperis equations by employing the direct algebraic method. These equations are used to investigate the (2+1)-dimensional interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis and the stability of the one-soliton solution of the well-known Korteweg–de Vries (KdV) equation under transverse perturbations. Since the wavelength of weakly dispersive, nonlinear waves is longer than their amplitude and their variations in the second spatial dimension (rescaled y) are slower than those in the principal propagation direction (rescaled x), the studied models’ soliton wave solutions are used to describe wave dynamics. Many solutions are obtained and demonstrated by plotting them in 2D, 3D, and contour plots. The implemented analytical scheme’s performance verifies its effectiveness and power. All solutions’ accuracy is checked by putting them back into their original model.

Keywords

• Nonlinear evolution equations
• Computational wave solutions
• Fluid mechanic