Similarity Transforming Techniques of Partial Differential Equations and its Applications: A review

Rashed, A. S.; Kassem, M. M.

doi:10.21608/dusj.2023.318647

Similarity Transforming Techniques of Partial Differential Equations and its Applications: A review

Document Type : Original research papers

Authors

A. S. Rashed ¹
M. M. Kassem ²

¹ Department of Physics and Engineering Mathematics Department, Faculty of Engineering, Zagazig university, Egypt. Faculty of Engineering, Delta University for Science and Technology, Gamasa, Egypt

² Department of Physics and Engineering Mathematics Department, Faculty of Engineering, Zagazig university, Egypt.

10.21608/dusj.2023.318647

Abstract

The current paper is a review of some transformation techniques of partial differential equations (PDEs) using similarity techniques which have the ability to reduce the number of independent variables to be a single variable resulting in a simpler ordinary differential equation (ODEs). These techniques have the benefit to obtain some completely new solutions. The paper introduces a summary and literature review for method of characteristic lines, Bäcklund transformations, Cole-Hopf Transformation, Lie infinitesimals, Non-classical symmetry method, Potential Symmetry, direct methods and characteristic function method.

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Main Subjects