9 citations · 21 across the 7 of their papers we have counts for
8 papers · 1 filter
Two soliton solutions to the three dimensional gravitational Hartree equation
Joachim Krieger, Yvan Martel, Pierre Raphael
We construct non dispersive two soliton solutions to the three dimensional gravitational Hartree equation whose trajectories asymptotically reproduce the nontrapped dynamics of the…
Asymptotic stability of solitons for the Benjamin-Ono equation
C. E. Kenig, Y. Martel
In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solution…
Stability of two soliton collision for nonintegrable gKdV equations
Yvan Martel, Frank Merle
We continue our study of the collision of two solitons for the subcritical generalized KdV equations. In a previous paper, mainly devoted to the case of the quartic gKdV equation,…
Description of two soliton collision for the quartic gKdV equation
Yvan Martel, Frank Merle
This paper concerns the problem of collision of two solitons for the quartic generalized Korteweg-de Vries equation. We introduce a new framework to describe the collision in the s…
Refined asymptotics around solitons for gKdV equations
Yvan Martel, Frank Merle
We consider the generalized Korteweg-de Vries equation with general nonlineari…
Asymptotic stability of solitons of the gKdV equations with general nonlinearity
Yvan Martel, Frank Merle
We consider the generalized Korteweg-de Vries equation \partial_t u + \partial_x (\partial_x^2 u + f(u))=0, \quad (t,x)\in [0,T)\times \mathbb{R}, (1) with general nonlineari…