Nonlinear Systems and Complexity
Volume 1 / 2012 to Volume 38 / 2023
Page
%P
31 Result(s)
within
Panayotis G. Kevrekidis
-
Article
Open AccessOn the Temporal Tweezing of Cavity Solitons
Motivated by the work of Jang et al., Nat Commun 6:7370 (2015), where the authors experimentally tweeze cavity solitons in a passive loop of optical fiber, we study the amenability to tweezing of cavity solitons ...
-
Article
Open AccessObservation of dense collisional soliton complexes in a two-component Bose-Einstein condensate
Solitons are nonlinear solitary waves which maintain their shape over time and through collisions, occurring in a variety of nonlinear media from plasmas to optics. We present an experimental and theoretical s...
-
Book Series
-
Book
-
Article
On the generation and propagation of solitary waves in integrable and nonintegrable nonlinear lattices
We investigate the generation and propagation of solitary waves in the context of the Hertz chain and Toda lattice, with the aim to highlight the similarities, as well as differences between these systems. We ...
-
Chapter
Nonlinearity and Topology
The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose–Einstein condensates, photonic...
-
Chapter
\(\phi ^4\) Solitary Waves in a Parabolic Potential: Existence, Stability, and Collisional Dynamics
We explore a \(\phi ^4\) model with an added external parabolic potential term. This term dramatically alters the spectral prop...
-
Chapter
Discrete Breathers in \(\phi ^4\) and Related Models
In this chapter, we touch upon the wide topic of discrete breathers with a special emphasis on the prototypical system of interest, namely the ...
-
Chapter
Discrete Variants of the \(\phi ^4\) Model: Exceptional Discretizations, Conservation Laws and Related Topics
Exceptional dicretizations of the \(\phi ^4\) model are reviewed, corresponding conservation laws are reported, and the propert...
-
Article
Open AccessInteractions and scattering of quantum vortices in a polariton fluid
Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems h...
-
Chapter
Dispersive Shock Waves
Shock waves are nonlinear structures characterized by a discontinuous jump in the wave profile. There exist prototypical examples of partial differential equations (PDEs), including the well-known Burgers’ equ...
-
Chapter
Discrete (Dark) Breathers
As indicated in the introductory chapter, discrete breathers are one of the most prototypical excitations that can arise in nonlinear dynamical lattices. They are periodic in time and strongly localized in spa...
-
Chapter
Media with Onsite Forces: The Newton’s Cradle and Beyond
In this section, we finally return to the Newton’s cradle shown in Fig. 1 and Fig. 28a. When the chain of balls is struck at one end, the ball on the opposite end is ejected from the chain, providing a nice il...
-
Chapter
Introduction and Motivation of Models
In the present short volume our aim will be to explore a variety of nonlinear wave structures that are found in a particular physical system, i.e., granular crystals. Many of the readers have almost certainly ...
-
Chapter
Higher Dimensional Lattices
Two-dimensional granular crystals have been investigated far less than 1D configurations. In two spatial dimensions, the nodes can be arranged in a number of ways. While the role of disorder is of particular i...
-
Chapter
Solitary Waves in the Nonlinear Dirac Equation
In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its l...
-
Chapter
Traveling Waves
Arguably, the most prototypical nonlinear wave structure that can arise in granular crystals consists of traveling waves. While many kinds of traveling waves exist (such as periodic ones [1]), in this chapter we ...
-
Chapter
Heterogeneous Media
Of the three primary structures of interest in this book, solitary waves and breathers have been studied in heterogeneous granular chains, while dispersive shock waves have not. The latter represents an area o...
-
Article
Open AccessTo infinity and some glimpses of beyond
When mathematical and computational dynamic models reach infinity in finite time, extending analysis and numerics beyond it becomes a notorious challenge. We suggest how, upon suitable transformations, it may ...
-
Article
Traveling Waves for the Mass in Mass Model of Granular Chains
In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely, a granular chain involving additionally an internal (or, respectively, external) resonator. For these ch...
