New Exact Solutions of the Brusselator Reaction Diffusion Model Using the Exp‐Function Method

Abstract

Firstly, using a series of transformations, the Brusselator reaction diffusion model is reduced into a nonlinear reaction diffusion equation, and then through using Exp-function method, more new exact solutions are found which contain soliton solutions. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The results show the reliability and efficiency of the proposed method.

Exact Traveling Wave Solutions for a Nonlinear Evolution Equation of Generalized Tzitzéica-Dodd-Bullough-Mikhailov Type

“…These exact solutions include smooth solitary wave solutions, singular periodic wave solutions of blow-up form, singular solitary wave solutions of blow-up form, broken solitary wave solutions, broken kink wave solutions, and some unboundary wave solutions. Comparing with the results in many references (such as [24][25][26][27]), these types of solutions in this paper are very different than those types of solutions which are obtained by Exp-function method. Though the types of solutions derived from two methods are different, they are all useful in nonlinear science.…”

“…Respectively, taking 0 = 0, (0) = 1 , and 0 = 0, (0) = 2 as initial values, substituting (26) into the / = of (11), and then integrating them yield…”

A mathematical modeling arising in the chemical systems and its approximate numerical solution

“…and so on; in this manner, the rest of the components of the homotopy perturbation solution can be obtained. The solutions u(x, y, t) and v(x, y, t) are given by truncated series (7) at the level N = 5 u x; y; t ð Þ¼…”

“…1 − A + B 2 > 0 . During the past few decades, many researchers studied the existence of solutions of the Brusselator reaction model using many methods …”

“…[3] During the past few decades, many researchers studied the existence of solutions of the Brusselator reaction model using many methods. [4][5][6][7][8][9][10] Considerable attention has been devoted to the study of the fractional calculus during the past three decades and their numerous applications in the area of physics and engineering. The applications of fractional calculus used in many fields such as electrical networks, control theory of dynamical systems, probability and statistics, electrochemistry of corrosion, chemical physics, optics and signal processing can be successfully modeled by linear or nonlinear fractional order differential equations.…”