Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation

Willy Hereman is Emeritus Professor of Applied Mathematics and Research Professor Emeritus in the Department of Applied Mathematics and Statistics at the Colorado School of Mines. He received his Bachelor's (1974), Master's (1976), and Ph.D. (1982) degrees in  Applied Mathematics from the University of Ghent, Belgium. He has held NATO Research Fellowships at the Department of Electrical and Computer Engineering of The University of Iowa and a Visiting Assistant Professorship in the Department of Mathematics at the University of Wisconsin-Madison. From 2011 to 2016, he served as Head of the Department of Applied Mathematics and Statistics at the Colorado School of Mines. He has published over a hundred research papers in acousto-optics, scattering theory, soliton theory, nonlinear wave phenomena, wavelets, and symbolic methods for nonlinear partial differential equations and nonlinear lattices. Supported by the National Science Foundation of the United States of America, he has developed several symbolic software packages in Mathematica for the investigation of integrability, symmetries, conservation laws, and exact solutions of nonlinear differential and difference equations. He is a laureate of the Royal Academy of Sciences of Belgium and a member of the American Association for the Advancement of Science, the American Mathematical Society, the Society of Industrial and Applied Mathematics, and Sigma Xi -- the Scientific Research Honor Society.

Ünal Göktaş has been an Instructional Associate Professor in the Department of Computer Science and Engineering, Texas A&M University since 2023. He received his Bachelor’s degree in Mathematics from Bogazici University, Turkey in 1993. Continuing his graduate studies in the U.S.A., he received his Master’s and Ph.D. degrees in 1996 and 1998 from the Department of Mathematical and Computer Sciences at the Colorado School of Mines. After completing his doctoral studies, he worked at Wolfram Research, Inc. (Urbana-Champaign, Illinois) as a senior software developer and at the Department of Computer Engineering, Turgut Özal University (Turkey) as an associate professor. His research interests include bio-informatics, symbolic computing, soliton theory, and the development of algorithms for analytic and numerical solutions of differential and recurrence equations.