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Well-posedness for the Non-integrable Periodic Fifth Order KdV in Bourgain Spaces
Ryan McConnell
We study well-posedness for a non-integrable generalization of the fifth order KdV, the second member in the KdV heirarchy. In particular, we use differentiation-by-parts to establ…
Talbot Effect on the Sphere and Torus for
M. Burak Erdogan, Chi N. Y. Huynh, Ryan McConnell
We utilize exponential sum techniques to obtain upper and lower bounds for the fractal dimension of the graph of solutions to the linear Schrödinger equation on and…
Non-linear Smoothing for the Periodic Generalized Non-linear Schrödinger Equation
Ryan McConnell
We consider the periodic non-linear Schrödinger equation with non-linearity given by for odd in dimension . We first establish that the difference between t…
Global Attractor for the Periodic Generalized Korteweg-de Vries Equation Through Smoothing
Ryan McConnell
We establish a smoothing result for the generalized KdV (gKdV) on the torus with polynomial non-linearity, damping, and forcing that matches the smoothing level for the gKdV at $H^…