对称扰动理论在偏微分方程中的应用研究

非线性科学已经被广泛应用于数学、物理、化学、经济等领域。许多非线性现象都可以用非线性偏微分方程来很好地描述,所以得到非线性偏微分方程的解具有重要的意义。在研究非线性科学的同时,出现了一些带有扰动项的非线性偏微分方程。为了研究这种扰动偏微分方程,一些以对称理论为基础的扰动方法相继产生。本文主要研究对称扰动理论在偏微分方程中的应用,寻求偏微分方程的近似对称约化和无穷级数解。

Application to Partial Differential Equation Based on the Symmetry and Perturbation Theory

the nonlinear partial differential equations has important significance in the study of nonlinear science,at the same time,there are some with disturbance term nonlinear partial differential equations.In order to study the disturbance of partial differential equations,some to the symmetry theory based on perturbation methods have been developed.This paper mainly studies the symmetrical perturbation theory with application to partial differential equation for partial differential equations,approximate symmetry reduction and solution of infinite series.