Analysis of a class of potential Korteweg-de Vries-like equations

摘要

We analyze a class of third-order evolution equations, i.e. u(t) = f(x, u(x), u(xx)) u(xxx) + g(x, u(x), u(xx)) via the method of preliminary group classification. This method is a systematic means of analyzing the equation for symmetries. We find explicit forms of f and g, which allow for a larger dimensional Lie algebra of point symmetries.