5 papers · 1 filter
Infinite-order multisoliton solutions to the Benjamin--Ono equation and soliton resolution
Louise Gassot, Patrick Gérard
We construct a class of infinite-order multisoliton solutions of the Benjamin-Ono equation on the line, for which the initial data exhibits slow spatial decay. We prove that in the…
Global well-posedness for the ILW equation in for
Louise Gassot, Thierry Laurens
We prove that the intermediate long wave (ILW) equation is globally well-posed in the Sobolev spaces for . The previous record for well-posedness wa…
The third order Benjamin-Ono equation on the torus : well-posedness, traveling waves and stability
Louise Gassot
We consider the third order Benjamin-Ono equation on the torus $\partial_t u= \partial_x \left( -\partial_{xx}u-\frac{3}{2}u H\partial_x u - \frac{3}{2}H(u\partial_x u) + u^3 \righ…
On the orbital stability of a family of traveling waves for the cubic Schr{ö}dinger equation on the Heisenberg group
Louise Gassot
We consider the focusing energy-critical Schr{ö}dinger equation on the Heisenberg group in the radial case\[i\partial_t u-Δ_{\mathbb{H}^1} u=|u|^2u,\quadΔ_{\mathbb{H}^1}=\frac{1}{4…
On the radially symmetric traveling waves for the Schr{ö}dinger equation on the Heisenberg group
Louise Gassot
We consider radial solutions to the cubic Schr{ö}dinger equation on the Heisenberg group$$i\partial_t u - Δ_{\mathbb{H}^1} u = |u|^2u, \quadΔ_{\mathbb{H}^1} = \frac{1}{4}(\partial_…