A generalized exponential transform method for solving non-linear evolution equations of physical relevance

The purpose of the present paper is to introduce a new computational algebraic procedure that can easily be applied for solving non-linear partial differential equations (nPDE) especially the celebrated evolutions equations describing any time depended sequences.The crucial step needs an auxiliary variable satisfying special class of ordinary differential equations (ODE) of first order which are introduced new in this field for the first time.The validity and reliability of the method is tested by its application to some non-linear evolution equations leading to new class of solutions related with some new types of special functions.Otherwise, for practical use in science and engineering the algebraic construction of new class of solutions is of fundamental interest and moreover, the proposed approach convinced by its easiness and does not need tedious steps of evaluation and can be used without studying the whole theory.The possibility to write a symbolic software using any programming languages is given.Further, the algorithm works efficiently, is clear structured and can be used in any applications independently from the order and the non-linearity of the underlying nPDE.Therefore, the given novel algebraic method is suitable for a wider class of nPDE in order to augment the solution manifold by an alternative approach.