Abstract CONTENTS Introduction Chapter I. Compact surfaces of constant mean curvature 1.
Differential equations of constant mean curvature surfaces 2. Sphere. Hopf theorem 3 …

The development of the inverse scattering transform (IST) has made it possible to solve
certain physically significant nonlinear evolution equations [l]. The original ideas were …

Let us consider a small domain II in the complex plane, ze II and an immersion F: II–» R" of II
into Euclidean space. It is well known that if F is a conformal parametrization of a surface …

Abstract CONTENTS Introduction Chapter I. Reduction of Abelian integrals and theta
functions § 1. Abelian integrals and Riemann theta functions § 2. Reduction of Abelian …

The inverse scattering transform has been an extremely useful tool in the study of solitons.
Its utility results, to a large extent, from (i) the practical importance of these isolated, localized …

We degenerate the finite gap solutions of the KdV equation from the general formulation
given in terms of abelian functions when the gaps tend to points, to get solutions to the KdV …

Solutions presque périodiques et a N-solitons de l'équation hydrodynamique non linéaire
de Kaup Page 1 ANNALES DE L’IHP, SECTION A VB MATVEEV MI YAVOR Solutions …

To construct these tori we use the methods of the integrable equations. These methods were
already successfully applied [17, 24, 6, 7] to differential geometric classification of some …

We see that the recursion operator is a very useful and important object in the theory of
nonlinear evolution equations integrable by the IST method. On the one hand, the recursion …

The method of finite-gap integration was created to solve the periodic KdV initial problem. Its
development during last 30 years, combining the spectral theory of differential and …