CLASSIFICATION OF MULTILINEAR REAL QUADRATIC PARTIAL DIFFERENCE EQUATIONS LINEARIZABLE BY POINT AND HOPF–COLE TRANSFORMATIONS

Abstract

We use the conditions of linearizability by point and by Hopf–Cole transformations, introduced recently by the authors, to classify all real multilinear equations on a square lattice with at most quadratic nonlinearity. We find that, up to a linear transformation of the dependent variable and an exchange of the independent variables, only two equations in this class are linearizable by point transformations and none by Hopf–Cole transformations.