3 papers
nlin.PS2026
Dissipation-driven champion solitons in one-dimensional shallow-water waves
Ashleigh Simonis, Sergey Nazarenko, Jalal Shatah +1
In this paper, we identify a new mechanism for rogue wave formation in a shallow-water setting. We study a bidirectional shallow-water wave field in the context of the Kaup-Boussin…
math.AP2026
Invariant Manifolds for Capillary Waves and a Class of Quasilinear PDEs
Jalal Shatah, Chongchun Zeng
This paper studies the local stable and unstable manifolds of equilibria for quasilinear and fully nonlinear PDEs. These manifolds are fundamental objects in the analysis of local…
nlin.CD2026
Bidirectional shallow-water wave turbulence
Ashleigh Simonis, Sergey Nazarenko, Jalal Shatah +1
We study bidirectional one-dimensional (1-D) shallow-water waves within a class of Boussinesq equations, including the integrable Kaup-Boussinesq (KB) equation and a truncated-disp…