Modulational instability, multiple Exp-function method, SIVP, solitary and cross-kink solutions for the generalized KP equation

Abstract

The multiple Exp-function method is employed for seeking the multiple soliton solutions to the generalized (3+1)-dimensional Kadomtsev-Petviashvili (gKP) equation, where contains one-wave, two-wave, and triple-wave solutions. The periodic wave including (exponential, $ \cosh $ hyperbolic, and $ \cos $ periodic), cross-kink containing (exponential, $ \sinh $ hyperbolic, and $ \sin $ periodic), and solitary containing (exponential, $ \tanh $ hyperbolic, and $ \tan $ periodic) wave solutions are obtained. In continuing, the modulation instability is engaged to discuss the stability of obtained solutions. Also, the semi-inverse variational principle is applied for the gKP equation with four major cases. The physical phenomena of these received multiple soliton solutions are analyzed and demonstrated in figures by choosing the specific parameters. By means of symbolic computation these analytical solutions and corresponding rogue waves are obtained with the help of Maple software. Via various three-dimensional, curve, and density charts, dynamical characteristics of these waves are exhibited.