The momentous revolution in science precipitated by Isaac Newton's calculus soon revealed
the central role of partial differential equations throughout mathematics and its manifold …

The area of nonlinear dispersive partial differential equations (PDEs) is a fast developing
field which has become exceedingly technical in recent years. With this book, the authors …

The Schrödinger equation on a circle with an initially localized profile of the wave function is
known to give rise to revivals or replications, where the probability density of the particle is …

We use exponential sums to study the fractal dimension of the graphs of solutions to linear
dispersive PDE. Our techniques apply to Schrödinger, Airy, Boussinesq, the fractional …

In this paper, we study fractal solutions of linear and nonlinear dispersive partial differential
equation on the torus. In the first part, we answer some open questions on the fractal …

In this paper, the dispersive revival and fractalization phenomena for bidirectional dispersive
equations on a bounded interval subject to periodic boundary conditions and discontinuous …

We study the phenomenon of revivals for the linear Schrödinger and Airy equations over a
finite interval, by considering several types of non-periodic boundary conditions. In contrast …

We present and analyze a novel manifestation of the revival phenomenon for linear spatially
periodic evolution equations, in the concrete case of three nonlocal equations that arise in …

With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality
and intermittency of the family of generalized Riemann's non-differentiable functions R x 0 …

When posed on a periodic domain in one space variable, linear dispersive evolution
equations with integral polynomial dispersion relations exhibit strikingly different behaviors …