Workshop on Dynamical Systems: Theory, Modelling and AI 19–21 November 2025 

Day-1 programme

[Mathematical Methods for the treatment of Differential Equations (DEs)]

Lie Symmetries and Group Analysis of DEs, Integrable Systems and Painlevé Analysis, Geometric Theory of DEs and Modern Techniques for the treatment of DEs

Workshop Abstracts (Day 1)

Title: Recent Advances in Differential Equations and Symmetries

Speaker: Sibusiso Moyo (DVC: Research, Innovation and Postgraduate Studies, Stellenbosch University)

Bio: Professor Sibusiso Moyo holds a PhD in Mathematics from the University of Natal, Durban and a Masters  in Tertiary Education Management (with distinction) from the University of Melbourne, Australia.  She served in various capacities and levels at the Durban University of Technology (DUT) as Lecturer, Senior Lecturer, Associate Director and Associate Professor in the Department of Mathematics, Statistics and Physics, Director for Research and Postgraduate Support, acting DVC Engagement and  DVC Research, Innovation and Engagement (RIE) for 5 years, 2 months before joining. As DVCRIE, she was  responsible for research and innovation policy development, implementation and evaluation. Her areas of responsibility included the Directorates for Research and Postgraduate Support, Technology Transfer and Innovation, Cooperative Education, Research Centers and Institutes,  Corporate Affairs, Advancement and Alumni Relations, International Education and Partnerships, Engagement and the Knowledge Information Management Cluster.   She has  published extensively in international journals and presented at both international and national conferences in her field and is involved in the supervision of  Masters and Doctoral students and mentors a number of postgraduate students and emerging researchers. She was also responsible for developing staff  programmes for staff to complete their PhDs and delivering short courses on Research Methodology, Research Design, Data handling techniques and Modeling techniques.  She held an NRF Y-Rating from 2005 to 2009. Her current research projects involve applications using group theoretic techniques in problems arising from nonlinear phenomena with applications in Mathematical and Physical Sciences. In addition, her current areas of interest also extend to strategic research that aims to inform research and innovation policies within the higher education sector and tertiary education management areas.  She also is involved in a number of initiatives that promote mathematics amongst the youth and mentoring young women to become leaders in their chosen fields of interest. While at DUT She focused extensively on establishing the DUT Center for Entrepreneurship and Innovation as well as developing programmes for mentoring student entrepreneurs as part of DUT's drive to  ensure its graduates become job creators and not just job seekers. From 1st September 2022, She joined Stellenbosch University as the DVC Research, Innovation and Postgraduate Studies.

Title: The Invariance, Conservation Laws and Integration of Difference Equations

Speaker: Abdul Hamid Kara (University of the Witwatersrand, Johannesburg)

Bio: Abdul H Kara completed all his studies at Wits University and in all, but one year, has been at Wits from Junior Lecturer through to Professor; the one year being served as a school teacher. His PhD thesis involved a range of topics around the Symmetries of Differential Equations, Euler-Lagrange equations and their relationship with Conservation Laws. Abdul has published with collaborators from China, the US, Russia, Pakistan and with his students from SA and abroad. He continues to apply his work in mathematical physics, engineering and relativity and extend his ideas to Discrete Equations and Fractional Differential Equations.

Abstract: A vast amount of work has been done to extend the ideas and applications of symmetries to difference equations (∆Es) in a number of ways. In some cases, the ∆Es are constructed from the DEs in such a way that the algebra of Lie symmetries remains the same. As far as conservation laws of ∆Es goes, the work is more recent. Here, we construct symmetries and conservation laws for some ordinary ∆Es, utilise the symmetries to obtain reductions of the equations and show, in fact, that the notion of ‘association’ between these concepts can be analogously extended to, for now, ordinary ∆Es. That is, an association between a symmetry and first integral exists if and only if the first integral is invariant under the symmetry. Thus, a ‘double reduction’ of the ∆ E is possible.

Title: Painlevé Analysis, higher-order rogue waves and dispersive solitons for a new generalized nonlinear evolution equation using a Hirota's N-soliton method

Speaker: Sachin Kumar (University of Delhi, India)

Bio: Prof. Sachin Kumar is a Professor in the Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi. He obtained his Ph.D. degree from the Indian Institute of Technology (IIT) Roorkee in 2011. He began his academic career at Babasaheb Bhimrao Ambedkar University (A Central University) in 2011 as an Assistant Professor and later joined the University of Delhi in 2014. His primary research interests include Nonlinear Partial Differential Equations, Nonlinear Waves, Mathematical Modeling, and Nonlinear Dynamics. Prof. Kumar has guided eight Ph.D. and five M.Phil. scholars who have made significant research contributions. He has published over 150 research papers in high-impact, peer-reviewed journals, with more than 5950 citations and an h-index of 45. He has completed five major research projects and is currently working on two more. His research achievements have been widely recognized—he received India Top Cited Paper Awards from IOP Publishing in 2021 and 2023 and has been listed among the world’s top 2% of scientists by Stanford University, USA, for four consecutive years (2022, 2023, 2024, and 2025). In recognition of his contributions, he received the UAE-INDO Inspiring Scientist Award 2022 in Dubai. Prof. Kumar also served as an Associate Editor for Partial Differential Equations in Applied Mathematics (Elsevier) and acts as a reviewer for more than thirty-five international journals. He has delivered numerous invited talks, organized national and international conferences, and introduced innovative computational techniques for solving nonlinear evolution equations.

Abstract: We investigate the dynamics of energy spreading and thermalisation in a one-dimensional nonlinear Klein-Gordon lattice with long-range interactions and disorder. Pairwise in- teraction terms in the potential are scaled by 1/r^α, where r is the distance between lattice sites and α ≥ 0 is a parameter which governs the range of interactions. Using measures such as the participation number, second moment and entropy, we study how energy spreading through the lattice depends on the range of interaction by varying the α parameter. In addition, we study the normal modes of the linearised system to understand their influence on the energy spreading dynamics.

Title: Applications of Equivalence Transformations to Group Classification 

Speaker: Sergey V. Meleshko (Suranaree University of Technology, Thailand)

Bio: Sergey V. Meleshko received his M.S. from Novosibirsk State University and his Ph.D. from the Institute of Hydrodynamics in 1981, under the guidance of Prof. Nikolay N. Yanenko and Prof. Vasiliy P. Shapeev. In 1991, he defended his doctoral dissertation, titled Classification of Solutions with Degenerate Hodograph of the Gas Dynamic and Plasticity Equations, at the Institute of Mathematics and Mechanics (Sverdlovsk). Since 1979, he has held positions as a researcher, senior researcher, and leading researcher at the Institute of Theoretical and Applied Mechanics (Novosibirsk). Concurrently, he served as a professor at Novosibirsk State University, where, as of July 1991, he held the role of Vice Dean. In 1996, he joined Suranaree University of Technology, where he has supervised more than 25 Ph.D. students. His principal research interests include analytical methods for constructing exact solutions of partial differential equations—particularly the method of differential constraints and group analysis of differential equations—symbolic (analytical) computation, and mathematical and numerical modeling. He has co-authored over 250 papers, along with two books published by Springer and one book by Nauka, all focusing on methods for constructing exact solutions of differential and integro- differential equations.

Abstract: The presentation is devoted to the application of equivalence transformations to the group classification of differential equations. It includes our experience in finding generalized equivalence transformations and performing preliminary group classification. As the construction of an optimal system of subalgebras is an essential part of using equivalence transformations for group classification, this topic will also be discussed. Part of the talk will focus on overdetermined systems of partial differential equations. Both partial differential equations and integro-differential equations will be considered. The presentation includes applications to the Boltzmann equation, the construction of invariant solutions for Gromeka–Beltrami flows, and the analysis of flows of chemically reacting gases in Eulerian and Lagrangian variables (for both unsteady and steady flows).  

Title: Symmetry Analysis of the geodesic equations of the canonical connection: The n-dimensional case with r-dimensional abelian nilradical

Speaker: Ryad Ghanam (Virginia Commonwealth University, Qatar)

Bio: Prof. Ryad Ghanam joined the faculty of Virginia Commonwealth University in Qatar in 2014, following an extensive teaching career in the United States. Over eighteen years of academic experience, he has taught a wide spectrum of undergraduate and advanced mathematics courses, consistently employing an interactive and student-centered pedagogy. His primary research interests lie in Lie algebras and their applications to differential equations, an area in which he remains actively engaged. Dr. Ghanam has supervised numerous senior theses, several of which were presented by students at mathematics conferences. He also served for two years as a consultant on a NASA-funded STEM education grant, providing training for schoolteachers on effective approaches to teaching science, technology, engineering, and mathematics to younger learners. He continues to receive invitations to teach advanced mathematical concepts to students across different school levels, an outreach activity he values highly, as it reflects his commitment both to advancing pure mathematical research and to promoting excellence in mathematics education.

Abstract: In this talk, I will present our preliminary results about the classification of the symmetry Lie algebra of the geodesic equations of the canonical connection on Lie groups. We will present our results for the low-dimensional cases, the case where we have one and two co-dimensional abelian nilradical and the most general case where the algebra has an r co-dimensional abelian nilradical.

Title: A Solow-Swan framework for economic growth with memory effect

Speaker: Mathew O. Aibinu (University of Regina, Canada)
Bio: Dr. Mathew O. Aibinu is a Postdoctoral Fellow in the Department of Mathematics and Statistics, University of Regina, Canada. He holds a Ph.D. in Mathematical Science from the University of KwaZulu-Natal and works on mathematical modelling, optimization, high-performance computing, and algorithm development with applications in economics and advanced computing. His research has earned multiple distinctions, including the Wits Centennial Postdoctoral Fellowship (2023–2025) and the 2024 BANKSETA Award. 

Abstract: The Solow-Swan equation is a cornerstone in the development of modern economic growth theory and continues to attract significant scholarly attention. This study incorporates memory effects into the classical Solow-Swan model by introducing a formulation based on the Caputo fractional derivative. A comparative analysis is conducted between the integer-order and fractional-order versions of the model to examine the influence of fractional dynamics on capital accumulation. The findings reveal that the inclusion of a fractional-order derivative significantly affects the trajectory and long-term stability of capital, offering a more flexible and comprehensive framework for modeling economic growth processes.

Title: The effect of long range interactions on energy spreading in nonlinear, disordered Klein-Gordon chains

Speaker: Jean-Jacq du Plessis (University of Cape Town)

Bio: Jean-Jacq du Plessis is a PhD student in the Nonlinear Dynamics and Chaos Group at the University of Cape Town. His doctoral research is on the dynamics of one-dimensional Hamiltonian lattices with emphasis on the effect of long-range interactions.

Abstract: We investigate the dynamics of energy spreading and thermalisation in a one-dimensional nonlinear Klein-Gordon lattice with long-range interactions and disorder. Pairwise in- teraction terms in the potential are scaled by 1/r^α, where r is the distance between lattice sites and α ≥ 0 is a parameter which governs the range of interactions. Using measures such as the participation number, second moment and entropy, we study how energy spreading through the lattice depends on the range of interaction by varying the α parameter. In addition, we study the normal modes of the linearised system to understand their influence on the energy spreading dynamics.

Title: Reduction via the One Dimensional Optimal System of Subalgebras of their Lie Algebra for physically interesting Partial Deferential Equations 

Speaker: Ali Raza (Stellenbosch University)

Bio: Dr. Ali Raza earned his Ph.D. in Mathematics from the Abdus Salam School of Mathematical Sciences, Government College University Lahore, in June 2023. He joined the Lahore School of Economics in August 2023, where he spent two productive years engaged in teaching and research. In recognition of his scholarly contributions, he was awarded a prestigious postdoctoral fellowship at Stellenbosch University, which he commenced on August 1, 2025. 

Abstract: We investigate optimal systems of one-dimensional subalgebras in Lie algebra and their importance in differential equation symmetry reductions. We start with the history of Lie groups and symmetry, then examine their role in simplifying PDEs. To classify inequivalent symmetry generators, optimal systems are introduced. The optimal system for the wave equation is constructed and applied as an example.

Title: Approximate Solutions of Geomagnetic Dynamical System: Extended Center Manifold and  Criterion for Synchronization.

Speaker: Mohamed Tantawy (Faculty of Engineering, October 6 University, Giza, Egypt)

Bio: Dr. Mohamed Tantawy is an Assistant Professor in the Faculty of Engineering at October 6 University. He holds a Ph.D. in Applied Mathematical Sciences (2017), an M.Sc. in Applied Mathematics (2014), and a B.Sc. in Mathematical Sciences (2007). He serves on the Membership Committee of the African Society for Biomathematics (ASB). His research focuses on computational partial differential equations and dynamical systems, and he has published 40 journal articles and one book. Dr. Tantawy is currently co-supervising two master’s students in computational applied mathematics and one in dynamical systems. 

Abstract: In this work, we aim to derive approximate solutions for the nonlinear geomagnetic dynamical system by constructing the Picard iteration scheme, with numerous works exploring its various chaotic features. We have proven the convergence of the theorem for this scheme, which ensures that our iterative process will be close to the exact solution. Global bifurcation of the system components within the parameter space is considered. Numerical evaluations of the solutions are performed, accompanied by the visualization of both three-dimensional (3D) and two-dimensional (2D) phase portraits. The 3D portraits reveal hyperchaos, a phenomenon arising from the extreme sensitivity of a system's dynamical evolution to small changes in initial conditions. A criterion for the synchronization of the real and imaginary parts of the system is to establish a necessary condition. An approach is developed for constructing the extended center manifold, which is pivotal in analyzing the system's behavior.

Title: λ -symmetries for a simple second-order nonlinear equation.

Speaker: Slungile Tshibase (University of KwaZulu-Natal, Durban)

Supervisor: Keshlan Govinde (University of KwaZulu-Natal, Durban)

Bio: PhD Student at the University of KwaZulu-Natal, Durban

Abstract: Lie symmetries are very useful because they can be used to solve differential equations. However, many equations do not admit Lie symmetries. As a result, we need to consider extensions; the one we consider here is the idea of λ-symmetries. These symmetries generalise Lie symmetries by introducing a function λ to allow reduction of equations that do not admit Lie symmetries. We will study the λ-symmetries of second-order ordinary differential equations of the form y’’=f (x, y) through a classification perspective. We will provide functional forms of f that will admit λ-symmetries, and we will show how these symmetries can be used to solve those equations.

Title: Shock wave interactions for rate-type materials

Speaker: Akshay Kumar (Suranaree University of Technology, Thailand)

Bio: I, Dr Akshay Kumar, am a researcher specialising in hyperbolic partial differential equations and nonlinear wave phenomena. I earned my PhD from the University of Hyderabad, India, under the supervision of Prof. R. Radha. Currently, I am a Postdoctoral Researcher at Suranaree University of Technology (SUT), Thailand, having previously worked as a Postdoctoral Researcher at Tata Institute of Fundamental Research - Centre for Applicable Mathematics (TIFR CAM) and as a Senior Research Associate at National Council of Educational Research and Training (NCERT).

Abstract: In this talk, the rate-type material model, whose solution consists of shock and rarefaction waves as derived in [3], is considered to discuss the shock wave interactions that occurred in the double Riemann problem with non-constant initial data. It is observed that the solution to the double Riemann problem is ultimately (after interaction of shock waves) given through either a 1 -shock wave and a 2 -rarefaction wave or 1 -shock wave and 2 -shock wave or 1 -rarefaction wave and 2 -shock wave subject to the initial data.