October  2011, 4(5): i-iii. doi: 10.3934/dcdss.2011.4.5i

Preface

1. 

Nonlinear Dynamical Systems Group, Computational Science Research Center and Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720

2. 

Grupo de Física No Lineal, Departamento de Física Aplicada I, EU Politécnica, Universidad de Sevilla, c/ Virgen de África s/n, 41011-Sevilla, Spain

3. 

Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece

4. 

University of Massachusetts, Lederle Graduate Research Tower, Department of Mathematics and Statistics, Amherst, MA 01003

5. 

Grupo de Física No Lineal, Escuela Técnica Superior de Ingeniería Informática, Departamento de Física Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41012-Sevilla, Spain

Published  December 2010

This issue of Discrete and Continuous Dynamical Systems - Series S is a compilation of papers representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems. During the last two decades, an impressive volume of theoretical and experimental work has been devoted to the existence, stability and dynamics of such coherent structures. They have been identified as critical components of numerous continuous and discrete dynamical systems and, depending on the context (and their particular form), they may be referred to as solitons, instantons, kinks, breathers, or quodons, among many others. We nowadays think of such localized nonlinear excitations as being ubiquitous in nature due to their experimental realization in many diverse systems including, but not limited to, optical fibers and waveguide arrays, photonic crystals, Bose-Einstein condensates, molecular crystals, quasi-one-dimensional solids, Josephson-junctions and arrays thereof, layered silicates, micromechanical cantilever arrays, uranium crystals, pendulum arrays, water waves, electrical transmission lines, ferromagnetic and antiferromagnetic materials, granular crystals and so on. Additionally, they are also conjectured to play an important role in denaturation transitions and bubble formation in DNA, protein folding, atom ejection and defect migration in crystals, low-temperature reconstructive transformations, and many others. The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and "design" of novel applications.

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Citation: Ricardo Carretero-González, Jesús Cuevas Maraver, Dimitri J. Frantzeskakis, P.G. Kevrekidis, Faustino Palmero Acebedo. Preface. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : i-iii. doi: 10.3934/dcdss.2011.4.5i
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Christian Kanzow, Dong-Hui Li, Nobuo Yamashita. Preface. Numerical Algebra, Control and Optimization, 2011, 1 (1) : i-v. doi: 10.3934/naco.2011.1.1i

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Thorsten Koch, Xiaoling Sun. Preface. Numerical Algebra, Control and Optimization, 2012, 2 (4) : i-ii. doi: 10.3934/naco.2012.2.4i

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Eduard Feireisl, Mirko Rokyta, Josef Málek. Preface. Discrete and Continuous Dynamical Systems - S, 2008, 1 (3) : i-iii. doi: 10.3934/dcdss.2008.1.3i

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Carlos Castillo-Chavez, Gerardo Chowell. Preface. Mathematical Biosciences & Engineering, 2011, 8 (1) : i-vi. doi: 10.3934/mbe.2011.8.1i

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P. De Maesschalck, Freddy Dumortier, Martin Wechselberger. Preface. Discrete and Continuous Dynamical Systems - S, 2009, 2 (4) : i-iii. doi: 10.3934/dcdss.2009.2.4i

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Urszula Ledzewicz, Marek Galewski, Andrzej Nowakowski, Andrzej Swierniak, Agnieszka Kalamajska, Ewa Schmeidel. Preface. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : i-ii. doi: 10.3934/dcdsb.2014.19.8i

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Cheng-Chew Lim, Song Wang. Preface. Journal of Industrial and Management Optimization, 2008, 4 (1) : i-ii. doi: 10.3934/jimo.2008.4.1i

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Vadim Kaloshin, Sergey Lototsky, Michael Röckner. Preface. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : i-ii. doi: 10.3934/dcdsb.2006.6.4i

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Wei Kang, Liang Ke, Qi Wang. Preface. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : i-i. doi: 10.3934/dcdsb.2007.8.3i

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Noureddine Alaa, Marc Dambrine, Antoine Henrot, Alain Miranville. Preface. Communications on Pure and Applied Analysis, 2012, 11 (6) : i-ii. doi: 10.3934/cpaa.2012.11.6i

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Shengji Li, Nan-Jing Huang, Xinmin Yang. Preface. Numerical Algebra, Control and Optimization, 2011, 1 (3) : i-ii. doi: 10.3934/naco.2011.1.3i

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Zhaosheng Feng, Jinzhi Lei. Preface. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : i-iv. doi: 10.3934/dcdsb.2011.16.2i

[20]

Frédéric Coquel, Edwige Godlewski, Jean-Marc Hérard, Jacques Segré. Preface. Networks and Heterogeneous Media, 2010, 5 (3) : i-ii. doi: 10.3934/nhm.2010.5.3i

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