CAJ | 학술논문

本文基于微分形式吴方法,给出了确定含小参数偏微分方程的两种近似对称的算法.算法的核心是克服了求解确定方程组的困难,这是确定偏微分方程近似对称的关键一步.作为算法的应用,给出了扰动KdV方程的近似对称及相应的近似不变解,这是吴方法在微分方程领域中的新应用.
본문기우미분형식오방법,급출료학정함소삼수편미분방정적량충근사대칭적산법.산법적핵심시극복료구해학정방정조적곤난,저시학정편미분방정근사대칭적관건일보.작위산법적응용,급출료우동KdV방정적근사대칭급상응적근사불변해,저시오방법재미분방정영역중적신응용.
In this article,an algorithm for determining two kinds of approximate symmetries of partial differential equations with a small parameter is proposed based on the differential form of Wu's method.The essence of the algorithm lies in how to overcome the difficulty of solving the determining equations,which is a key step to obtain approximate symmetry of PDEs.As applications of the algorithm,the approximate symmetries and corresponding approximate invariant solutions to a perturbed KdV equation are determined.This is a new application of Wu's method in the field of differential equations.