Strong-field effects in laboratory and astrophysical plasmas and high intensity laser and
cavity systems are considered, related to quantum electrodynamical (QED) photon-photon …

The collapse of self-focusing waves described by the nonlinear Schrödinger (NLS) equation
and the Zakharov equations in nonlinear optics and plasma turbulence is reviewed. Special …

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 …

Modern laser sources nowadays deliver ultrashort light pulses reaching few cycles in
duration and peak powers exceeding several terawatt (TW). When such pulses propagate …

Optical collapse is a fascinating research topic. The propagation of intense laser beams in a
transparent medium is usually modeled by the two-dimensional nonlinear Schrödinger …

We investigate the properties of localized waves in cubic nonlinear materials with a
symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality …

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 consider the problem of identifying sharp criteria under which radial H 1 (finite energy)
solutions to the focusing 3d cubic nonlinear Schrödinger equation (NLS) i∂ tu+ Δ u+| u| 2 u …

The formation of singularities of self-focusing solutions of the nonlinear Schrödinger
equation (NLS) in critical dimension is characterized by a delicate balance between the …

Two alternative scenarios pertaining to the evolution of nonlinear wave systems are
considered: solitons and wave collapses. For the former, it suffices that the Hamiltonian be …