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 …

Turing patterns are commonly understood as specific instabilities of a spatially
homogeneous steady state, resulting from activator–inhibitor interaction destabilized by …

Abstract The Korteweg‐de Vries equation, Boussinesq equation, and many other equations
can be formally derived as approximate equations for the two‐dimensional water wave …

We are interested in the long-time behaviour of nonlinear parabolic PDEs defined on
unbounded cylindrical domains. For dissipative systems defined on bounded domains, the …

Nonlinear modulation of gravity-capillary waves travelling principally in one direction at the
surface of a three-dimensional fluid leads to the Davey-Stewartson system for the wave …

Abstract The Ginzburg–Landau equation (GLe)∂ t A= div [(I+ i S)∇ A]+ ρ A− c ˆ| A| 2 A, with
A (t, x)∈ ℂ, t⩾ 0, x∈ ℝ d, appears in many different contexts, eg, nonlinear optics with …

We investigate the formation of optical extreme waves in a resonant two-level medium that
entails the self-induced transparency (SIT) effect, within the framework of the sine-Gordon …

Counter-propagating Waves on Fluid Surfaces and the Continuum Limit of the Fermi-Pasta-Ulam
Model 1 Introduction Page 1 Counter-propagating Waves on Fluid Surfaces and the Continuum …

We are interested in the nonlinear stability of the Eckhaus-stable equilibria of the Swift-
Hohenberg equation on the infinite line with respect to small integrable perturbations. The …

The purpose of this paper is to rigorously derive the cubic–quintic Ginzburg–Landau
equation as a modulation equation for the stochastic Swift–Hohenberg equation with cubic …