3 papers
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…
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…
math.NA2025
A New Approach to Direct Discretization of Wave Kinetic Equations with Application to a Nonlinear Schrodinger System in 2D
J. W. Banks, J. Shatah
Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new…