计算机技术与发展2017，Vol.27Issue(11)：196-200,5.DOI:10.3969/j.issn.1673-629X.2017.11.042
辅助函数法求解非线性偏微分方程精确解
Auxiliary Function Method for Exact Solution of Nonlinear Partial Differential Equation
摘要
Abstract
In mathematics and physics,a nonlinear partial differential equation is a partial differential equation with nonlinear terms,which can describe many different physical models ranging from gravitation to fluid dynamics,and have been adopted in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. There are almost no general solutions that can be applied for all equa-tions. Nonlinear partial differential equation usually originates from mathematical and physical fields,such that the ansatz of the solutions has been given and an auxiliary function has been provided according to its mathematical and physical features. They can be transmitted to an ordinary differential equations via a traveling wave transformation. Through introduction of the auxiliary function into the ordinary dif-ferential equation a set of nonlinear algebra equations is acquired,which can supply solutions original partial differential equation in sol-ving process. Therefore,BBM equation and Burgers equation can be solved with the auxiliary function. The exact solutions include tan-gent function and trigonometric functions. The research shows that the proposed auxiliary function method can be applied to solve some other nonlinear partial differential equations with mathematical and physical background.关键词
非线性偏微分方程/辅助函数法/BBM方程/Burgers方程/精确解Key words
nonlinear partial differential equation/auxiliary function method/BBM equation/Burgers equation/exact solution分类
信息技术与安全科学引用本文复制引用
杨健,赖晓霞..辅助函数法求解非线性偏微分方程精确解[J].计算机技术与发展,2017,27(11):196-200,5.基金项目
国家自然科学基金资助项目(11471004) （11471004）
