61 citations · 228 across the 17 of their papers we have counts for
21 papers
Hamiltonian reduction using a convolutional auto-encoder coupled to an Hamiltonian neural network
Raphaël Côte, Emmanuel Franck, Laurent Navoret +2
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the…
Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation
Raphaël Côte, Xu Yuan
We consider the nonlinear damped Klein-Gordon equation \[ \partial_{tt}u+2α\partial_{t}u-Δu+u-|u|^{p-1}u=0 \quad \text{on} \ \ [0,\infty)\times \mathbb{R}^N \] with , $2 \le N…
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…
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 \[ \partial_{t}^{2}u+2α\partial_{t}u-\partial_{x}^{2}u+u-|u|^{p-1}u=0 \quad \mbox{on ,}\]…
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…
Description and classification of 2-solitary waves for nonlinear damped Klein-Gordon equations
Raphaël Côte, Yvan Martel, Xu Yuan +1
We describe completely 2-solitary waves related to the ground state of the nonlinear damped Klein-Gordon equation \begin{equation*} \partial_{tt}u+2α\partial_{t}u-Δu+u-|u|^{p-1}u=0…