In these lecture notes I consider one remarkable system of differential equations that
appeared in the papers of physicists on two-dimensional topological field theory (TFT) in the …

Abstract CONTENTS Introduction Chapter I. Hamiltonian theory of systems of hydrodynamic
type § 1. General properties of Poisson brackets § 2. Hamiltonian formalism of systems of …

There is growing physical and mathematical interest in the hydrodynamics of
dissipationless/dispersive media. Since GB Whitham's seminal publication fifty years ago …

There has been a revolution in nonlinear physics over the past twenty years. Two great
discoveries, each of which, incidentally, was made with the aid of the computer experiment …

The authors introduce a new concept of measure-valued solution for the 3-D incompressible
Euler equations in order to incorporate the complex phenomena present in limits of …

In 438 alphabetically-arranged essays, this work provides a useful overview of the core
mathematical background for nonlinear science, as well as its applications to key problems …

We review the spectral theory of soliton gases in integrable dispersive hydrodynamic
systems. We first present a phenomenological approach based on the consideration of …

The complete classification of solutions to the defocusing complex modified KdV equation
with step-like initial condition is studied by the finite-gap integration approach and Whitham …

I. One-dimensional systems of hydrodynamic type. Poisson brackets and Riemannian
geometry. From a purely mathematical point of view many systems such as ideal fluids …

In Part I the scattering transform method is used to study the weak limit of solutions to the
initial value problem for the Korteweg-deVries (KdV) equation as the dispersion tends to …