Browsing Bergen Open Research Archive by Author "Pilod, Didier Jacques Francois"
Now showing items 1-5 of 5
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Dispersive Estimates for Full Dispersion KP Equations
Selberg, Sigmund; Pilod, Didier Jacques Francois; Saut, Jean-Claude; Temesgen, Achenef Tesfahun (Journal article; Peer reviewed, 2021)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 ... -
Full family of flattening solitary waves for the critical generalized KdV equation
Martel, Yvan; Pilod, Didier Jacques Francois (Journal article; Peer reviewed, 2020)For the critical generalized KdV equation ∂tu+∂x(∂2xu+u5)=0 on R, we construct a full family of flattening solitary wave solutions. Let Q be the unique even positive solution of Q′′+Q5=Q. For any ν∈(0,13), there exist ... -
On the unique continuation of solutions to non-local non-linear dispersive equations
Kenig, C.E.; Pilod, Didier Jacques Francois; Ponce, G.; Vega, L. (Journal article; Peer reviewed, 2020)We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if u1,u2 are two suitable solutions of the equation defined in Rn×[0,T] such that ... -
Unconditional uniqueness for the Benjamin-Ono equation
Mosincat, Razvan-Octavian; Pilod, Didier Jacques Francois (Journal article, 2023)We study the unconditional uniqueness of solutions to the Benjamin–Ono equation with initial data in Hs, both on the real line and on the torus. We use the gauge transformation of Tao and two iterations of normal form ... -
Well-Posedness for the Extended Schrödinger–Benjamin–Ono System
Linares, Felipe; Mendez, Argenis J.; Pilod, Didier Jacques Francois (Journal article; Peer reviewed, 2024)