61 citations · 108 across the 22 of their papers we have counts for
29 papers
Continuum of finite point blowup rates for the critical generalized Korteweg-de Vries equation
Yvan Martel, Didier Pilod
For any , we prove the existence of an solution of the mass critical generalized Korteweg-de Vries equation on the time interval , for so…
Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation
Luc Molinet, Didier Pilod, Stéphane Vento
We consider the Cauchy problem associated to a class of dispersive perturbations of Burgers' equations, which contains the low dispersion Benjamin-Ono equation, (also known as low…
On the Benjamin and related equations
C. Klein, F. Linares, D. Pilod +1
We consider in this paper various theoretical and numerical issues on classical one dimensional models of internal waves with surface tension.They concern the Cauchy problem, inclu…
Well-posedness for the extended Schrödinger-Benjamin-Ono system
Felipe Linares, Argenis Mendez, Didier Pilod
In this work we prove that the initial value problem associated to the Schrödinger-Benjamin-Ono type system \begin{equation*} \left\{ \begin{array}{ll} \mathrm{i}\partial_{t}u+ \pa…
Breather Solutions to the Cubic Whitham Equation
Henrik Kalisch, Miguel A. Alejo, Adán J. Corcho +1
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 str…
Unconditional uniqueness for the Benjamin-Ono equation
Razvan Mosincat, Didier Pilod
We study the unconditional uniqueness of solutions to the Benjamin-Ono equation with initial data in , both on the real line and on the torus. We use the gauge transformatio…