Bright and dark soliton solutions of three-dimensional KdV and mKdV equations in inviscid liquid with gas bubbles

Abstract

Mixture of liquid with gas bubbles are found in many areas of natural and physical sciences especially in engineering and industries, where nonlinear wave propagation is a common phenomenon. In this paper, we obtained the bright and dark soliton solutions of the three-dimensional Korteweg-de-Vries (KdV) equation and three-dimensional modified Korteweg-de-Vries (mKdV) equation in an inviscid bubbly liquid flow. Bright soliton solutions of these equations were derived analytically using a secant hyperbolic wave ansatz, while the dark soliton solutions of the equations were obtained explicitly using tan-gent hyperbolic wave ansatz. The physical parameters in the soliton solutions are obtained.