Biography

My enduring passion for mathematics has motivated me to pursue a career focused on exploring how mathematical principles can address complex issues. The intricate nature and rapid evolution of this field continuously inspire me. My Bachelor’s and Master’s degrees in Mathematics have equipped me with the essential problem-solving skills and in-depth subject knowledge required for effective mathematical research. Engaging in my honours project on “Application of Linear Algebra in Cryptography” and my Master’s thesis on “Analytical Methods to Nonlinear Models: Soliton Solution Perspectives” has further solidified my commitment and dedication to this discipline. I am honoured to share that my article, titled “Novel Dynamics of the Fokas-Lenells Model in Birefringent Fibers Applying Different Integration Algorithms,” has been published in the International Journal of Mathematics and Computer in Engineering.

Educational Details

Experiences

Research Interest

Nonlinear Dynamics, Soliton theory, Optics, Bifurcation Analysis, Nonlinear PDE model, Cryptography.

IT Skills

MATLAB | LATEX | Python | FORTRAN | MATHEMATICA | MAPLE | Microsoft (Word, Excel, PowerPoint)

Language Skills

I have both a Bachelor of Science and Master of Science degree in English as my primary language of Instruction.

Project & thesis

Project on “Application of Linear Algebra in Cryptography” This project focuses on the encoding and decoding of messages which is known as cryptography technique regarding linear algebra and number theory. A general overview of cryptography is provided and two special types of algorithm (hill cipher and affine cipher) are discussed in this paper. The basis linear operation system, the terms of number theory which is used in cryptography is also discussed here. Two main feature of cryptography- encryption and decryption are noted in details in terms of hill cipher and affine cipher. All encryption and decryption process of hill cipher and affine cipher have been coded in MATLAB programming language. Thesis on “Analytical Methods to Nonlinear Models: Soliton Solution Perspectives” A wide range of natural phenomena can be represented by nonlinear modeling. In the domain of nonlinear science, a highly potent field is found in soliton theory, which encompasses various phenomena including solitons, multi-solitons, rational functions, breather lines, breather kinks, lumps, and rogue wave solutions. These solutions play a crucial role in uncovering the intrinsic characteristics of nonlinear models. This dissertation has been presented exact traveling wave solutions of the four nonlinear models such as the (𝟏 + 𝟏)-dimensional Fokas Lenells model, the (𝟏 + 𝟏)-dimensional long-wave–short-wave resonance interaction model, the (𝟐 + 𝟏)- dimensional Zoomeron model, and the (𝟑 + 𝟏)-dimensional Jimbo-Miwa equation by applying various integration algorithms. A variable transformation is applied to convert these model's partial differential equations into ordinary differential equations. Subsequently, these governing models are processed using the above-mentioned methods with Maple-18 software. Various novel dynamical optical solitons are generated through solutions. The dynamic behaviors of the acquired outcomes are vividly illustrated through density, 2D and 3D graphical representations via the computational software Maple 18.

Seminar

Seminar on “The nonlinear evolution equation in Mathematical Physics and Biology” [October 12, 2022] Nonlinear evolution equations are essential in understanding various phenomena in mathematical physics. They are more complex and challenging than linear equations, leading to diverse behaviors not finding linear systems. Key concepts include nonlinearity, which refers to systems where output is not directly proportional to input and types like nonlinear, integral, and partial differential equations. These equations have applications in wave propagation, chaos theory, and solitons. Studying nonlinear equations has led to discovery new mathematical techniques, such as perturbation methods and numerical simulations. Understanding these equations is crucial for advancing knowledge involving pure mathematics and applied physics.

Publication

Jahan M. I., Ullah M.S., Roshid H. O., Rahman Z.,Akter R.(2024). Novel Dynamics of the Fokas-Lenells model in birefringent fibers applying different integration algorithms, International Journal of Mathematics and Computer in Engineering 3(1),1-12. doi:10.2478/ijmce.2025-0001 (https://sciendo,com/article/10.2478/ijmce-2025-0001)

Award

1st position in the 1st Intra-Batch Math Olympiad Competition-2023

Scholarships

1. National Science and Technology (NST) Fellowship-2023

2. Vice Chancellor Scholarship-2023