In this text the authors consider the Korteweg-de Vries (KdV) equation (ut=-uxxx+ 6uux) with
periodic boundary conditions. Derived to describe long surface waves in a narrow and …

The goal of geometric numerical integration is the simulation of evolution equations
possessing geometric properties over long periods of time. Of particular importance are …

Our goal in this monograph is twofold. First, we would like to develop a robust method to
construct global time-quasiperiodic solutions of large families of quasilinear evolution …

In this paper, we establish the existence of time quasi-periodic solutions to generalized
surface quasi-geostrophic equation $({\rm gSQG}) _\alpha $ in the patch form close to …

We consider the cubic defocusing nonlinear Schrödinger equation on the two-dimensional
torus. Fix s> 1. Recently Colliander, Keel, Staffilani, Tao and Takaoka proved the existence …

In this paper we prove that the Benjamin‐Ono equation, when considered on the torus, is an
integrable (pseudo) differential equation in the strongest possible sense: this equation …

We consider the cubic nonlinear Schrödinger (NLS) equation as well as the modified
Korteweg–de Vries (mKdV) equation in one space dimension. We prove that for each s>− 1 …

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation
| Probability Theory and Related Fields Skip to main content SpringerLink Log in Menu Find a …

The lecture notes cover the emergence of generalized hydrodynamics for the classical and
quantum Toda chain, the classical Calogero fluid, the Ablowitz-Ladik discretization of the …

Ablowitz and Ladik discovered a discretization that preserves the integrability of the
nonlinear Schrödinger equation in one dimension. We compute the generalized free energy …