Course description

Attendance

It is mandatory to attend at least 80% of lectures and at least 80% of problem sessions. Failure to do so without an official attendance waiver will lead to an F grade for the course.

Problem sessions

• PS1, PS2

Projects

Projects will involve studying a paper of interest, writing a report, and giving a brief oral presentation (15 minutes) at the end of the course. Below are some suggested project topics with brief descriptions. Each pair of students is expected to prepare one project.

1. Soliton molecules in Fermi-Pasta-Ulam-Tsingou lattice: Gardner equation approach, M. Kirane and S. Stalin and R. Arun and M. Lakshmanan [arXiv:2308.16535]
2. Multi‐Hamiltonian structure of the Born–Infeld equation, Arik, M., Neyzi, F., Nutku, Y., Olver, P.J. and Verosky, J.M., Journal of mathematical physics, 30(6), pp.1338-1344 (1989) [link]
3. Solvable Structures for Hamiltonian Systems, Kresic-Juric, Sasa, Concepcion Muriel, and Adrian Ruiz, [arXiv:2504.02189]
4. Integral invariants of the Hamilton equations, Kozlov, V. V, Mathematical Notes, 58(3), 938-947 (1995) [link]
5. Integrable scattering theory with higher derivative Hamiltonians, Andreas Fring and Bethan Turner, Eur. Phys. J. Plus 138 (2023) no.12, 1136 [arXiv:2307.15210].
6. Quasi-isospectral higher-order Hamiltonians via a reversed Lax pair construction, Francisco Correa, Andreas Fring [2507.19622]
7. PT-symmetric Deformations of the Korteweg-de Vries Equation, Andreas Fring, J. Phys. A 40 (2007), 4215-4224 [math-ph/0701036]
8. Dispersive Fractalization in Fermi–Pasta–Ulam Lattices I. The Linear Regime, P.Olver [link]
9. Hamiltonian formulation of the KdV equation, Y. Nutku, Journal of Mathematical Physics, 25(6), 2007-2008 (1984) [link]