Daniel Kraus's Home Page

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I was conferred a Ph.D. in Mathematics by the University at Buffalo in 2014 (advisor: Gino Biondini). At UB, I was a student, teaching assistant, tutor, instructor, and researcher. After graduating, I continued doing research whilst pursuing other, non-academic professional interests. Starting in July 2016, I will be a visitor in the Department of Mathematics & Statistics at Brock University, where I will be working with Stephen Anco and Thomas Wolf. If you are an old friend looking to catch up, or if you would like to discuss my research with me, please feel free to contact me via email.


Contact Information

Email: dkkraus@buffalo.edu


Research

My research focuses on using the inverse scattering transform (IST) to find exact soliton solutions of the vector nonlinear Schrödinger equation (a partial differential equation) with nonzero boundary conditions at infinity. The execution of the IST relies heavily on complex analysis and linear algebra, which are favorite subjects of mine.

Curriculum Vitae


Publications

"The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions", with G. Biondini and B. Prinari, Commun. Math. Phys. 348, 475–533 (2016)

"Polarization interactions in multi-component defocusing media", with G. Biondini, B. Prinari, and F. Vitale, J. Phys. A 48, 395202 (2015)

"The focusing Manakov system with non-zero boundary conditions", with G. Biondini and G. Kovacic, Nonlinearity 28, 3101–3151 (2015)

"Inverse scattering transform for the defocusing Manakov system with non-zero boundary conditions", with G. Biondini, SIAM J. Math. Anal. 47, 706–757 (2015)

Last updated: January 19, 2017