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

Authors: Lanfang Zhang; Juanjuan Ji; Julang Jiang; Chaolong Zhang

Addresses: School of Physics and Electrical Engineering, Anqing Normal University, Anqing Anhui, China ' School of Physics and Electrical Engineering, Anqing Normal University, Anqing Anhui, China ' School of Physics and Electrical Engineering, Anqing Normal University, Anqing Anhui, China ' School of Physics and Electrical Engineering, Anqing Normal University, Anqing Anhui, China

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.

Keywords: (3 + 1)-dimensional time fractional KZK equation; diffraction; thermoviscous attenuation; nonlinearity; fractional complex transform; numerical simulation.

DOI: 10.1504/IJCSM.2019.098744

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.2, pp.174 - 192

Received: 29 Mar 2017
Accepted: 19 Jul 2017
Published online: 02 Apr 2019 *

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