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Microscopic conservation laws for integrable lattice models
Benjamin Harrop-Griffiths, Rowan Killip, Monica Visan
We consider two discrete completely integrable evolutions: the Toda Lattice and the Ablowitz-Ladik system. The principal thrust of the paper is the development of microscopic conse…
Local well-posedness for a quasilinear Schrödinger equation with degenerate dispersion
Benjamin Harrop-Griffiths, Jeremy L. Marzuola
We consider a quasilinear Schrödinger equation on for which the dispersive effects degenerate when the solution vanishes. We first prove local well-posedness for suffic…
Compactons and their variational properties for degenerate KdV and NLS in dimension 1
Pierre Germain, Benjamin Harrop-Griffiths, Jeremy L. Marzuola
We analyze the stationary and traveling wave solutions to a family of degenerate dispersive equations of KdV and NLS-type. In stark contrast to the standard soliton solutions for n…
Finite depth gravity water waves in holomorphic coordinates
Benjamin Harrop-Griffiths, Mihaela Ifrim, Daniel Tataru
In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the…