Zobrazeno 1 - 10
of 117
pro vyhledávání: '"Pilod, Didier"'
Autor:
Pilod, Didier, Valet, Frédéric
We study the dynamics of the collision of two solitary waves for the Zakharov-Kuznetsov equation in dimension $2$ and $3$. We describe the evolution of the solution behaving as a sum of $2$-solitary waves of nearly equal speeds at time $t=-\infty$ up
Externí odkaz:
http://arxiv.org/abs/2403.02262
Autor:
Pilod, Didier, Valet, Frédéric
We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov-Kuznetsov equation in dimensions two and three. Moreover, we derive a qualitative version of the orbital stability result which turns out to be useful f
Externí odkaz:
http://arxiv.org/abs/2312.17721
We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity $s = -\frac 12$ as the critical regularity for ILW with any depth parameter, by establish
Externí odkaz:
http://arxiv.org/abs/2311.08142
We study the well-posedness issue of the intermediate long wave equation (ILW) on both the real line and the circle. By applying the gauge transform for the Benjamin-Ono equation (BO) and adapting the $L^2$ well-posedness argument for BO by Molinet a
Externí odkaz:
http://arxiv.org/abs/2311.07997
In this work we prove that the initial value problem associated to the Schr\"odinger-Benjamin-Ono type system \begin{equation*} \left\{ \begin{array}{ll} \mathrm{i}\partial_{t}u+ \partial_{x}^{2} u= uv+ \beta u|u|^{2}, \partial_{t}v-\mathcal{H}_{x}\p
Externí odkaz:
http://arxiv.org/abs/2308.02373
We are concerned with numerical approximations of breather solutions for the cubic Whitham equation which arises as a water-wave model for interfacial waves. The model combines strong nonlinearity with the non-local character of the water-wave proble
Externí odkaz:
http://arxiv.org/abs/2201.12074
Autor:
Mosincat, Razvan, Pilod, Didier
Publikováno v:
Pure Appl. Analysis 5 (2023) 285-322
We study the unconditional uniqueness of solutions to the Benjamin-Ono equation with initial data in $H^{s}$, both on the real line and on the torus. We use the gauge transformation of Tao and two iterations of normal form reductions via integration
Externí odkaz:
http://arxiv.org/abs/2110.07017
Autor:
Martel, Yvan, Pilod, Didier
In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of sufficient conditions for blowup, the stability of blowup in
Externí odkaz:
http://arxiv.org/abs/2107.00268
This paper focuses on the Dysthe equation which is a higher order approximation of the water waves system in the modulation (Schr\"{o}dinger) regime and in the infinite depth case. We first review the derivation of the Dysthe and related equations. T
Externí odkaz:
http://arxiv.org/abs/2007.01613
We prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev-Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev-Petviashvili equations. The proof of these estimates combines
Externí odkaz:
http://arxiv.org/abs/2005.08789