The Discrete Nonlinear Schrödinger Equation

Mathematical Analysis, Numerical Computations and Physical Perspectives

Authors:

ISBN: 978-3-540-89198-7 (Print) 978-3-540-89199-4 (Online)

Table of contents (24 chapters)

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  1. Front Matter

    Pages i-xviii

  2. I Dimensions and Components

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-9

      General Introduction and Derivation of the DNLS Equation

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      Book Chapter

      Pages 11-53

      The One-Dimensional Case

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      Book Chapter

      Pages 55-98

      The Two-Dimensional Case

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      Book Chapter

      Pages 99-116

      The Three-Dimensional Case

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      Book Chapter

      Pages 117-141

      The Defocusing Case

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      Book Chapter

      Pages 143-152

      Extended Solutions and Modulational Instability

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      Book Chapter

      Pages 153-171

      MultiComponent DNLS Equations

  3. II Special Topics

    1. Front Matter

      Pages 173-173

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      Book Chapter

      Pages 175-189

      Experimental Results Related to DNLS Equations

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      Book Chapter

      Pages 191-203

      Numerical Methods for DNLS

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      Book Chapter

      Pages 205-220

      The Dynamics of Unstable Waves

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      Book Chapter

      Pages 221-233

      A Map Approach to Stationary Solutions of the DNLS Equation

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      Book Chapter

      Pages 235-247

      Formation of Localized Modes in DNLS

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      Book Chapter

      Pages 249-257

      Few-Lattice-Site Systems of Discrete Self-Trapping Equations

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      Book Chapter

      Pages 259-275

      Surface Waves and Boundary Effects in DNLS Equations

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      Book Chapter

      Pages 277-291

      Discrete Nonlinear Schrödinger Equations with Time-Dependent Coefficients (Management of Lattice Solitons)

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      Book Chapter

      Pages 293-310

      Exceptional Discretizations of the NLS: Exact Solutions and Conservation Laws

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      Book Chapter

      Pages 311-327

      Solitary Wave Collisions

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      Book Chapter

      Pages 329-351

      Related Models

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      Book Chapter

      Pages 353-368

      DNLS with Impurities

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      Book Chapter

      Pages 369-377

      Statistical Mechanics of DNLS

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