Abstract This work is dedicated to putting on a solid analytic ground the theory of local well-posedness for two dimensional Dysthe equation. equation can be derived from incompressible Navier–Stokes after performing an asymptotic expansion wavetrain modulation fourth order. Recently, this has been used numerically study rare phenomena large water bodies such as rogue waves. In order well-posed...

The spectrum of a Schrödinger operator with a perfect honeycomb lattice potential has special points, called Dirac points where the lowest two branches of the spectrum touch. Deformations can result in the merging and disappearance of the Dirac points and the originally intersecting dispersion relation branches separate. Corresponding to these deformations, nonlinear envelope equations are deri...