Breather, lump, shock and travelling-wave solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics

Investigation is conducted on a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid mechanics and plasma physics. By virtue of the homoclinic-test, ansatz and polynomial-expansion methods, we construct the breather and lump solutions, shock wave solutions and travelling-wave solutions, respectively. We observe that the breather propagates steadily along a straight line with certain angles with the x, y and z axes. We observe that the amplitude and shape of the bright-dark lump wave keep unchanged during the propagation. We observe that the amplitude and the shape of the shock wave keep unchanged during the propagation. We graphically analyse the effects of the coefficients in the equation on the breather, lump and shock waves. We find that the lump is the most stable while the shock wave is the least stable under the same perturbation among the breather, lump and shock waves.