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math.AP2020
On smoothness and uniqueness of multi-solitons of the non-linear Schr{ö}dinger equations
Raphaël Côte, Xavier Friederich
In this paper, we study some properties of multi-solitons for the non-linear Schr{ö}dinger equations in R^d with general non-linearities. Multi-solitons have already been construct…
math.AP2020★ 16 cited
Long-time asymptotics of the one-dimensional damped nonlinear Klein-Gordon equation
Raphaël Côte, Yvan Martel, Xu Yuan
For the one-dimensional nonlinear damped Klein-Gordon equation \[ \partial_{t}^{2}u+2α\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on ,}\]…
math.AP2020
Polynomial Growth of high Sobolev Norms of solutions to the Zakharov-Kuznetsov Equation
Raphaël Cote, Frédéric Valet
We consider the Zakharov-Kuznetsov equation (ZK) in space dimension 2. Solutions u with initial data u\_0 H s are known to be global if s 1. We prove that for any integ…