topics. However, only a modest preliminary knowledge is needed. In the first chapter, where
we introduce an important topological concept, the so-called topological degree for …

Page 1 The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse Catherine
Sulem Pierre-Louis Sulem Springer Page 2 Applied Mathematical Sciences Volume 139 Editors …

This book presents in a self-contained form the typical basic properties of solutions to
semilinear evolutionary partial differential equations, with special emphasis on global …

Conservation laws arise from the modeling of physical processes through the following three
steps: 1) The appropriate physical balance laws are derived for m-phy-t cal quantities, ul""' …

We study the long-time behavior of small solutions of the initial-value problem for the
generalized Korteweg-de Vries equation∂ t u+∂ x 3 u+∂ x F (u)= 0 (gKdV) u (x, 0)= g (x) …

An acceptable modification of some Sobolev spaces is found in order to obtain a useful
decay rate in a nonlinear wave equation. Since the decay is dependent on invariance of the …

In this paper we consider the Vlasov Poisson equation in three space variables in the whole
space. We show the existence of dispersion property. With this dispersion property we are …

This book is the second edition of the book Lectures on nonlinear evolution equations. Initial
value problems [150] from 1992. Additionally, it now includes a new Chapter 13 on initial …

It is shown that the initial value problem for the nonlinear Schrödinger equations∂ tu= i Δ u+
P (u,∇ xu, u¯,∇ xu¯), t∈ ℝ, x∈ ℝ n, where Ρ (.) is a polynomial having no constant or linear …

On étudie le problème de Cauchy associéà une equation de Schrödinger non linéaire
modélisant une impulsion laser ultra-intense et ultra-courte dans un plasma. Les termes non …