The new exact analytical solutions and numerical simulation of (3 + 1)-dimensional time fractional KZK equation

Abstract

The KZK parabolic nonlinear wave equation is one of the most widely employed nonlinear models for propagation of 3D diffraction sound beams in dissipative media. In this paper, the exact analytical solutions of (3 + 1)-dimensional time fractional KZK equation have been constructed in the sense of modified Riemann-Liouville derivative and the (G′/G)-expansion method, the simplest equation and the fractional complex transform. As a result, some new exact analytical solutions are obtained, and the effects of diffraction, attenuation and nonlinearity are researched deeply using the obtained exact analytical solutions.