Abstract The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear
equations in the physics community. It describes a vast variety of phenomena from nonlinear …

Abstract Complex Ginzburg–Landau (CGL) equations serve as canonical models in a great
variety of physical settings, such as nonlinear photonics, dynamical phase transitions …

One of the major problems in the study of evolution equations of mathematical physics is the
investigation of the behavior of the solutions to these equations when time is large or tends …

This book gives an introduction to the mathematical theory of cooperative behavior in active
systems of various origins, both natural and artificial. It is based on a lecture course in …

An exploratory technique is introduced for investigating how much of the irregularity in an
aperiodic time series is due to low dimensional chaotic dynamics, as opposed to stochastic …

Interaction of slightly overlap** solitary pulses (SP's) is considered in the cubic nonlinear
Schrödinger equation with small pum** and dissipation terms, and in the quintic Ginzburg …

We evaluate several alternative methods for the approximation of inertial manifolds for the
one-dimensional Kuramoto-Sivashinsky equation (KSE). A method motivated by the …

The high dimensionality and complex dynamics of turbulent flows remain an obstacle to the
discovery and implementation of control strategies. Deep reinforcement learning (RL) is a …

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to
attractors that exist on finite-dimensional manifolds. We present a data-driven reduced-order …

Abstract The generalized complex Ginzburg-Landau equation,∂ t A= RA+ (1+ iv) δA-(1+ iμ)¦
A¦ 2σ A, has been proposed and studied as a model for “turbulent” dynamics in nonlinear …