Preliminary group classification of equations <i>v</i> <i>t</i> <i>t</i>=<i>f</i> (<i>x</i>,<i>v</i> <i>x</i>)<i>v</i> <i>x</i> <i>x</i>+<i>g</i>(<i>x</i>,<i>v</i> <i>x</i>)

Abstract

A classification is given of equations vtt=f(v,vx)vxx+g(x,vx) admitting an extension by one of the principal Lie algebra of the equation under consideration. The paper is one of few applications of a new algebraic approach to the problem of group classification: the method of preliminary group classification. The result of the work is a wide class of equations summarized in Table II.