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• #### Instability of the solitary waves for the generalized Boussinesq equations ﻿

(Peer reviewed; Journal article, 2020)
In this work, we consider the following generalized Boussinesq equation \begin{align*} \partial_{t}^2u-\partial_{x}^2u+\partial_{x}^2(\partial_{x}^2u+|u|^{p}u)=0,\qquad (t,x)\in\R\times \R, \end{align*} with $0<p<\infty$. ...
• #### Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations ﻿

(Peer reviewed; Journal article, 2020)
In this work, we consider the following generalized derivative nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\partial_{xx} u +i |u|^{2\sigma}\partial_x u=0, \quad (t,x)\in \R\times \R. \end{align*} We prove ...