Project Description

The research project "Nonlinear dispersive equations: nonlocal operators, dispersive blow-up and the soliton resolution conjecture" (NonDispEq) is founded by the Trond Mohn Stiftelse (TMS) and hosted at the Department of Mathematics of the University of Bergen. It was launched in 2018 and aims at expanding our knowledge of dynamic properties of solutions to nonlinear dispersive evolution equations arising in mathematical physics and mathematical fluid mechanics.

News and Events

• Master defense of Torunn Stavland Jensen, May 31 2024.

•  2024 Bergen-Lund-Trondheim workshop on dispersive and water waves equations, Bergen, Norway, April 27-28,2024.

• PhD defense of Martin Oen Paulsen, April 26 2024. 

• PhD defense of Arnaud Eychenne, January 13 2023. 

• 2nd Norwegian meeting on PDEs, Bergen, Norway, June 8-10, 2022. 

• Dispersive Waves and related topics, conference in honor of Gilles Lebeau, Bergen, June 17-21, 2019. 

•  1st Norwegian meeting on PDEs, Trondheim, Norway, June 5-7, 2019.

• Analysis and PDE seminar at UiB (every Tuesday from 14:15 to 16:00 at UiB)

• One-day seminar on Geometry, Analysis, and PDE Bergen, October 21, 2018.

Publications and Preprints

1. Dynamics of the collision of two nearly equal solitary waves for the Zakharov-Kuznetsov equation,  preprint (2024), 72 pages,  Didier Pilod and Frédéric Valet. 

2. Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation,  preprint (2024), 32 pages, Didier Pilod and Frédéric Valet. 

3. On the Benjamin and related equations,  preprint (2023), 26 pages, Christian Klein, Felipe Linares, Didier Pilod and Jean-Claude Saut. 

4. Justification of the Benjamin-Ono equation as an internal water waves model, preprint (2023), 84 pages, Martin Oen Paulsen.

5. Intermediate long wave equation in negative Sobolev spaces, preprint (2023), 15 pages, Andreia Chapouto, Justin Forlano, Guopeng Li, Tadahiro Oh and Didier Pilod. 

6. Deep-water limit of the intermediate long wave equation in L^2, preprint (2023), 26 pages, Andreia Chapouto, Guopeng Li, Tadahiro Oh and Didier Pilod.

7.  Rigorous derivation of weakly dispersive shallow water models with large amplitude topography variations, preprint (2023), 45 pages, Louis Emerald and Martin Oen Paulsen. 

8.  The long time well-posedness and full justification of a Whitham-Green-Naghdi system, preprint (2023), 37 pages, Louis Emerald and Martin Oen Paulsen. 

9. Well-posedness for the extended Schrödinger-Benjamin-Ono system, to appear in Vietnam Journal of Mathematics, preprint (2023), 22 pages, Felipe Linares, Argenis Mendez and Didier Pilod.

10. Strongly interacting solitary waves for the fractional modified Korteweg-de Vries equation, Journal of Functional Analysis, 285 (2023), no. 11, Paper No. 110145, 71 pages, Arnaud Eychenne and Frederic Valet. 

11. Decay of solitary waves of fractional Korteweg-de Vries Type equations, Journal of Differential Equations, 363 (2023), 243-274,  Arnaud Eychenne and Frederic Valet.

12. Asymptotic N-soliton-like solutions of the fractional Korteweg-de Vries equation, Rev. Mat. Iberoam, 39 (2023), no 5, 1813-1862, Arnaud Eychenne. 

13. Long time well-posedness of Whitham-Boussinesq systems, Nonlinearity, 35 (2023), no 12, 6284-6348, Martin Oen Paulsen.

14. Unconditional uniqueness for the Benjamin-Ono equation, Pure&Applied Analysis, 5 (2023), 285–322, Razvan Mosincat and Didier Pilod.

15. Finite point blowup for the critical generalized Korteweg-de Vries equation, to appear in Annali Scuola Normale Superiore - Classe di Scienze, preprint (2021), 41 pages, Yvan Martel and Didier Pilod.

16. Global well-posedness and scattering for the Dysthe equation in L^2, J. Math. Pures Appl., 149 (2021), 73–97, Razvan Mosincat, Didier Pilod and Jean-Claude Saut.

17. Dispersive estimates for full dispersion KP equations, J. Math. Fluid Mech., 23 (2021), paper no. 25, 24 pp, Didier Pilod, Jean-Claude Saut, Sigmund Selberg and Achenef Tesfahun

18. Full family of flattening solitary waves for the mass critical generalized KdV equation, Comm. Math. Phys., 378, (2020),1011-1080, Yvan Martel and Didier Pilod.

19. On the unique continuation of solutions to non-local non-linear dispersive equations, Comm. Part. Diff. Eq., 45 (2020), no. 8, 872-886, Carlos Kenig, Didier Pilod, Gustavo Ponce and Luis Vega.

20. On the local well-posedness for a full dispersion Boussinesq system with surface tension, Proc. Amer. Math. Soc., 147 (2019), 2545-2559, Henrik Kalisch and Didier Pilod.