MSc. Mathematics and Statistics (Mathematics)
Research Advisor: Professor Stephen Anco
Program Entry Date: Fall 2016
What is your current status in the program? I have graduated from the program
Research Title: Integrable 2-component peakon equations from a modified AKNS scheme.
Research Topic
My area of research is Mathematical Physics, which is description and modeling of physical problems using mathematics. I worked on a special class of water waves in mathematics and physics known as peakons.
Peakons arise in the theory of shallow water waves. They are traveling waves whose amplitude has a sharp corner at the peak. This shape is maintained as the wave propagates. Peakons are a model for waves that can be seen in the shallow waters near a beach. Apart from being solutions of water-wave equations, they also occur in other nonlinear equations in which waves have a special kind of dispersive feature. Some of these equations have many remarkable mathematical properties — even though the equations are nonlinear, they can be solved exactly by recasting them into an equivalent matrix (array) form that satisfies a certain geometrical condition known as zero-curvature. Such kinds of nonlinear equations with peakon solutions are very rare and finding new examples is of tremendous interest.
Now what happens when two different types of peakon waves interact? How do they behave? Is there an equation to describe the interaction? My research answered these questions. My research obtained new nonlinear equations that describe the interaction of two different types of peakon waves and that can be solved exactly. For future research, it will be very interesting to explore their peakon solutions and discover how the two types of peakon waves interact with each other.
What have you learned in your graduate education that you would share with future or current students?
Determination, hard-work and diligence are the keys for a successful student. There are times you need to work harder than ever to achieve your goal. Any good thing does not come on a silver platter and therefore working hard pays at the end.
What makes Brock stand out for you?
Two things make Brock stand out for me.
- The community nature. The size of Brock makes it easy to connect with others. There are always opportunities to ensure students succeed in their academic and professional careers. Brock is like a family; students’ success is everyone’s goal.
- The professors are very open and ready to help students succeed. I had one-on-one access to my professors, making it easy to the get the help needed. Also, the professors are always working hard, being on top of publications which encourages students to work hard.
What are your tips for thriving in grad school?
One thing I did was being open and stepping out of my comfort zone. There are opportunities at Brock for students to get involved and add values/experiences to their graduate degree. The Brock community is always open to help students succeed and I took advantage of that. Even though I was an international student, I didn’t feel like one. It felt like home to me.
What were the best parts of your experience at Brock? Why?
The best part of my experience is the opportunity to get involved with the community and the connections I made. I also had the opportunity to serve my fellow students as Vice President International for Graduate Students Association and as International ambassador for the university. It was a good feeling to be involved in the community, with students and faculty. Being involved in the community helped me know the people and connected with them.
Also, the opportunity to work with a renowned professor in the area that interested me. Working under his supervision was a great experience.
What would you do differently if you could do it over again?
I will repeat what I did. I don’t think I have any regrets or something I left behind undone. I had my Brock experience to it fullness.
Do you feel your degree has prepared you for your plans academically and otherwise?
Yes. I have had the best research experience and training I needed to pursue PhD research or to do independent work. With the strong supervision and teaching from the department, I am confident that I can work independently in the area.