Exact Solutions of the Modified Nonlinear Burgers' Equation

Q3 Mathematics

WSEAS Transactions on Systems and Control Pub Date : 2023-12-21 DOI:10.37394/23203.2023.18.50

Bubpha Jitsom, S. Sungnul, E. Kunnawuttipreechachan

引用次数: 0

Abstract

The expansion approach has been used to solve the modified nonlinear Burgers' equation, which has a nonlinear convection term, a viscosity term, and a time-dependent term in its structure. In this paper, the main focus is to find exact solutions of the modified nonlinear Burgers' equation. The (G′=G)-expansion method is one of the methods used to find exact solutions of nonlinear problems. It requires an appropriate transform equation to convert partial differential equations to ordinary differential equations, making it easier to find the solution. In this work, we choose the traveling wave equation to covert the equation. The results show that the exact solutions of the modified nonlinear Burgers' equation by the (G′=G)-expansion method are decreasing if traveling wave parameter, ω, increases for the first case and the exact solution is increasing if ω is increasing for the second case. It is observed that (G′=G)-expansion method is an advanced and easy tool for finding exact solutions of the modified nonlinear Burgers' equation.

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修正非线性布尔格斯方程的精确解

扩展法被用于求解修正的非线性布尔格斯方程，该方程的结构中包含一个非线性对流项、一个粘性项和一个随时间变化的项。本文的重点是寻找修正的非线性布尔格斯方程的精确解。(G′=G)- 展开法是用于寻找非线性问题精确解的方法之一。它需要一个适当的变换方程将偏微分方程转换为常微分方程，从而更容易求解。在这项工作中，我们选择行波方程来转换方程。结果表明，在第一种情况下，如果行波参数ω增大，用（G′=G）展开法求得的修正非线性布尔格斯方程的精确解是递减的；在第二种情况下，如果ω增大，精确解是递增的。由此可见，(G′=G)-展开法是寻找修正非线性布尔格斯方程精确解的一种先进而简便的工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

WSEAS Transactions on Systems and Control Mathematics-Control and Optimization

CiteScore

1.80

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Systems and Control publishes original research papers relating to systems theory and automatic control. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with systems theory, dynamical systems, linear and non-linear control, intelligent control, robotics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.