An overview of the dynamics of one of the fundamental models of low-dimensional nonlinear
physics, the Frenkel–Kontorova (FK) model, is presented. In its simplest form, the FK model …

This work systematically investigates a large number of oscillatory network configurations
that are able to describe many real systems such as electric power grids, lasers or even the …

Based on chaos theory two very important points are clear:(I) random looking aperiodic
behavior may be the product of determinism, and (2) nonlinear problems should be treated …

Surveying both theoretical and experimental aspects of chaotic behavior, this book presents
chaos as a model for many seemingly random processes in nature. Basic notions from the …

In this paper we develop new global perturbation techniques for detecting homoclinic and
heteroclinic orbits in a class of four dimensional ordinary differential equations that are …

We study the externally driven damped nonlinear Schrödinger equation on an infinite line.
The existence and stability chart for its soliton solution is constructed on the plane of two …

9.5. A priori estimates of the dimension of the attractor 339 11. New trends in the theory of
dissipative structures 349 10. Elementary types ofordering in two-dimensional systems 339 …

This paper explores the utility of a discrete singular convolution (DSC) algorithm for the
integration of the sine-Gordon equation. The initial values are chosen close to a homoclinic …

In this paper the homoclinic geometric structure of the integrable sine-Gordon equation
under periodic boundary conditions is developed. Specifically, focus is given to orbits …

Surface wave data from the Adriatic Sea are analysed in the light of new data analysis
techniques which may be viewed as a nonlinear generalization of the ordinary Fourier …