On the Connection of Lambert Functions and Classes of Solutions of Nonlinear Evolution Equations

In this paper a new algebraic procedure is introduced to compute new classes of solutions of (1+1)-nonlinear partial differential equations (nPDEs) of scientific and technical relevance. The crucial step of the method is the basic assumption that the unknown solution of the nPDE under consideration satisfies an ordinary differential equation (ODE) of the first order that can be integrated completely. A further important aspect of this paper however is the fact that we have the freedom in choosing some parameters bearing positively on the algorithm. So the solutionmanifold of any nPDE under consideration is augmented naturally. Since Lambert function involves several classes of unknown solutions in terms of further special functions could obtain. The present algebraic procedure can widely be used to study several nPDEs and is not only restricted to time-dependent problems. We note that no numerical methods are necessary and so closed-form analytical classes of solutions result. The algorithm works accurately, is clear structured and can be converted in any computer language. On the contrary it is worth to stress out the necessity of such sophisticated methods since a general theory of nPDEs does not exist.