Tobibur RahmanTobibur Rahman
I study how noise and memory reshape nonlinear waves.
I derive soliton solutions of fractional and stochastic partial differential equations, analyse their stability, bifurcations and chaos, and test them in simulation. Five journal articles so far, and I am preparing to apply for doctoral study in applied mathematics in the United States.
M.S. in Mathematics (in progress) and B.Sc. in Mathematics, HSTU · Research Assistant, Department of Mathematics, since March 2023
- Field
- Fractional and stochastic PDEs, soliton dynamics, scientific computing
- Affiliation
- Department of Mathematics, HSTU, Dinajpur, Bangladesh
- ORCID
- 0009-0008-5649-4982
- Journal articles
- 5 peer-reviewed, 2024 to 2026
- Journals
- Scientific Reports, Chaos, Solitons & Fractals, Opt. Quantum Electron.
- Conference presentations
- 5, including 4 oral talks
- Current study
- M.S. in Mathematics, HSTU, since June 2026
On this site
Research
Solitons of fractional and stochastic PDEs: exact solutions, stability, bifurcation and chaos, and the numerics behind them.
Publications
Five peer-reviewed articles in Scientific Reports, Chaos, Solitons & Fractals and Optical and Quantum Electronics, each with a figure and a plain summary.
Simulation lab
Change the fractional order and the noise intensity and watch a soliton respond, as a heat map or a rotating 3D surface.
Contact
Email, ORCID and Scholar, and a short message form for collaboration or supervision enquiries.
CV
Education, research experience, four conference presentations, olympiad honours, skills and referees.
Publications
-
Scientific Reports · 2026Solitons, bifurcation, chaos, and stability of the fractional Schrödinger–Hirota equation with beta derivative
Optical pulses in dispersive fibre, modelled by the Schrödinger–Hirota equation with a β-fractional derivative. The study derives new exact solitons and then asks a dynamical question: when does the system stop behaving regularly?
-
Chaos, Solitons & Fractals · 2026 · open accessFrom Hertzian contact to Pochhammer–Chree dynamics: solitons, chaos, and bifurcation in granular metamaterials
A chain of elastic beads touching through Hertzian contact carries stress waves that no linear model captures. The paper connects the discrete Hertz law to a continuum Pochhammer–Chree equation with cubic nonlinearity.
-
Optical and Quantum Electronics · 2026Soliton solutions, chaotic dynamics, and stability analysis of the (2+1)-dimensional time–space fractional nonlinear Schrödinger equation
A two-dimensional nonlinear Schrödinger model with fractional derivatives in both space and time, relevant to optical pulse transport, plasma oscillation and fluid flow.
-
Optical and Quantum Electronics · 2024Comprehensive soliton solutions of fractional stochastic Kraenkel–Manna–Merle equations in ferromagnetic materials
Short magnetic waves in ferrites, modelled by a Kraenkel–Manna–Merle system that carries both memory (conformable derivative) and randomness (multiplicative Brownian noise). My contribution covered software, data curation, formal analysis and writing.
-
Optical and Quantum Electronics · 2024 · open accessExclusive soliton solutions arise in mono-mode optical fibre connecting to nonlinear Fokas system
The (2+1)-dimensional Fokas system describes nonlinear pulses in mono-mode optical fibre, with separate parameters for dispersion, nonlinear coupling, transverse dispersion and saturation.
Simulation lab
Background
Education
- B.Sc. (Honours) in Mathematics, HSTU, 2022–2025
- Data Analysis with Python, EDGE Project, Bangladesh Computer Council, 2025
Experience
- Research Assistant to Prof. Dr. Md. Tarikul Islam since March 2023
- Co-author of five journal articles, 2024 to 2026
Honours
- 3rd place, Rangpur region, 13th National Undergraduate Mathematics Olympiad (2022)
- 6th place, Rangpur region, 16th National Undergraduate Mathematics Olympiad (2025)
Tools
- Python (NumPy, SciPy, SymPy, PyTorch), MATLAB, Maple, Mathematica
- Physics-informed neural networks, LaTeX, Git
Talks
- Jun 2026
Bifurcation, chaos and soliton dynamics in the fractional stochastic Ivancevic option pricing model: an econophysics perspective
Oral presentation, International Conference on Emerging Frontiers in Advanced Sciences and Technologies (EFAST 2026), Pabna University of Science and Technology. With M. T. Islam and M. A. Akbar
- Dec 2025
AI-driven analysis of the fractional stochastic Davey–Stewartson model in optical fibres, using analytical methods and physics-informed neural networks
Oral presentation, 24th International Mathematics Conference (24IMC 2025), University of Chittagong. With S. B. S. Jyoti, S. Ryehan and M. T. Islam
- Feb 2025
Exact soliton solutions, bifurcation, chaotic and multistability analysis for the modified Benjamin–Bona–Mahony equation
Poster, RURS 1st International Student Conference and Research Fair, University of Rajshahi. With M. M. I. Rhifat and M. T. Islam
- Feb 2025
The analytical solitary wave solutions and bifurcation analysis of the space–time fractional stochastic Yu–Toda–Sasa–Fukuyama equation, across conformable, beta and M-derivatives
Oral presentation, 3rd National Mathematics Conference 2024, BUET, Dhaka. With M. M. I. Rhifat, M. H. Ifti and M. T. Islam
- Dec 2023
Outstanding soliton solutions of the stochastic Konno–Oono model arising in a magnetic field with noise effects
Oral presentation, 1st National Conference on Advances in Science and Technology, BUET, Dhaka. With S. Ryehan and M. T. Islam
Get in touch
I welcome conversations with faculty and researchers working on nonlinear waves, fractional and stochastic PDEs, and scientific computing.