Nonlinearity with Disorder

1. Front Matter

   Pages I-XI

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2. Mathematical and Statistical Aspects

   1. Front Matter

      Pages 1-1

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   2. Linear Chaos

      • B. V. Chirikov

      Pages 3-13

   3. Second-Order Perturbations for Solitons

      • D. J. Kaup

      Pages 14-22

   4. Deformation of Solitons in Random Media

      • M. Wadati

      Pages 23-29

   5. Nonlinear Wave Propagation Through Disordered Media

      • Y. S. Kivshar

      Pages 30-44

   6. Nonlinearity and Disorder in the Statistical Mechanics of Integrable Systems

      • R. K. Bullough, J. Timonen, Yu-zhong Chen

      Pages 45-57

   7. Classical and Quantum Mechanical Analysis of Order and Chaos in the Discrete Self-Trapping Equation

      • P. L. Christiansen, L. Cruzeiro-Hansson, H. Feddersen, R. Flesch, M. Salerno, A. C. Scott

      Pages 58-66

   8. The Nonlinear Schrödinger Equation on a Disordered Chain

      • R. Scharf, A. R. Bishop

      Pages 67-84

   9. Dynamics of Sine-Gordon Soliton Interactions with Impurities

      • W. C. Kerr, A. R. Bishop, S. N. Kerr

      Pages 85-93

   10. Chaotic Dynamics of Nonlinear Schrödinger Soliton Interaction with an Oscillating Impurity

       • F. Kh. Abdullaev, A. A. Abdumalikov

       Pages 94-100

   11. Modulated Dark Soliton: Features of Creation and Propagation

       • V. V. Konotop, V. E. Vekslerchik

       Pages 101-114

   12. Dynamics of a Stochastically Perturbed φ ⁴ Model

       • A. Sánchez, L. Vázquez

       Pages 115-122

   13. On the Threshold of KdV Soliton Production

       • Kh. T. Kholmurodov

       Pages 123-125

   14. One-Dimensional Localization and Wave Propagation in Linear and Nonlinear Media

       • S. A. Gredeskul, L. A. Pastur

       Pages 126-133

   15. Annihilation of Topological Chiral Solitons

       • M. M. Musakhanov, I. V. Musatov

       Pages 134-142

   16. On Some Probabilistic Problems in the Theory of Quadratic Operators

       • T. A. Sarymsakov, N. N. Ganikhodzhaev

       Pages 143-149

   17. Superexponential Damping of Mean Field Propagating in Randomly Inhomogeneous Medium with Anomalously Large-Scale Nonuniformities

       • A. Yu. Val’kov, V. P. Romanov, T. I. Tipyasova

       Pages 150-158

3. Physical Applications

   1. Front Matter

      Pages 159-159

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   2. Nonlinearity, Disorder, the Spread of Neolithic Farming, and the Origin of the Indo-European Languages

      • M. H. Cohen

      Pages 161-170

In the past three decades there has been enormous progress in identifying the essential role that nonlinearity plays in physical systems, including supporting soliton-like solutions and self-trapped sxcitations such as polarons. during the same period, similarly impressive progress has occurred in understanding the effects of disorder in linear quantum problems, especially regarding Anderson localization arising from impurities, random spatial structures, stochastic applied fields, and so forth. These striking consequences of disorder, noise and nonlinearity frequently occur together in physical systems. Yet there have been only limited attempts to develop systematic techniques which can include all of these ingredients, which may reinforce, complement or frustrate each other. This book contains a range of articles which provide important steps toward the goal of systematic understanding and classification of phenomenology. Experts from Australia, Europe, Japan, USA, and the USSR describe both mathematical and numerical techniques - especially from soliton and statistical physics disciplines - and applicaations to a number of important physical systems and devices, including optical and electronic transmission lines, liquid crystals, biophysics and magnetism.

• DNA
• Disorder
• Noise
• Nonlinearity
• Solitons
• biophysics
• liquid crystal
• nonlinear dynamics
• protein
• statistical physics
• structure

• Thermal Physics Department, Uzbek Academy of Sciences, Tashkent-135, Chilanzar, Uzbekistan

  Fatkulla Abdullaev

• Los Alamos National Laboratories, Los Alamos, USA

  Alan R. Bishop

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