Solutions of Differential Equations by Symmetry Methods

This book is the outcome of my lecture notes of the graduate courses “Applications of Lie Groups I & II” given in Manisa Celal Bayar University. It also contains substantial material from my published papers on symmetries of differential equations. As a prerequisite, to gain the utmost benefit from the book, a familiarity with the knowledge of ordinary and partial differential equations and their solution techniques would be beneficial. The book can be considered as an introduction to the topic of symmetries of differential equations and how to use them to produce analytical solutions. It is intended to be a graduate textbook on the topic as well as a guide for researchers seeking for analytical solutions to their specific problems. The concentration is on the applications and solution techniques with the theory kept to a minimum so that the book can be readable by engineers and applied oriented researchers without much difficulty. At the end of each chapter, some exercises are also included so that the book can be adapted in a graduate course as a textbook. As a researcher with an engineering background, I became familiar with the symmetry methods during my Ph.D. studies under the supervision of late Prof. Erdoğan Şuhubi from Istanbul Technical University. His lectures and guidance of symmetry methods in the language of exterior differential forms was my initial familiarity with the topic. Later, I switched to the more classical and direct approach of the Lie group theory instead of calculating the symmetries via exterior differential forms. This book employs the direct classical approach of Lie groups to determine the symmetries of differential equations and finding their solutions. I hope the book will be beneficial to engineers, applied physicists and applied mathematicians who seek solutions to their problems.