Handbook of exact solutions to the nonlinear Schrödinger equations /

This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived e...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Khawaja, Usama (Autor), Sakkaf, Laila (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2020]
Colección:IOP ebooks. 2020 collection.
Temas:
Schrödinger equation.
Differential equations, Nonlinear.
Nonlinear wave equations.
Mathematical physics.
SCIENCE / Physics / Mathematical & Computational.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 1. Introduction
  • 2. Fundamental nonlinear Schrödinger equation
  • 2.1. NLSE with cubic nonlinearity
  • 2.2. Summary of subsection 2.1.1
  • 2.3. Summary of subsection 2.2.1
  • 3. Nonlinear Schrödinger equation with power law and dual power law nonlinearities
  • 3.1. NLSE with power law nonlinearity
  • 3.2. Summary of section 3.1
  • 3.3. NLSE with Dual power law nonlinearity
  • 3.4. Summary of section 3.3
  • 4. Nonlinear Schrödinger equation with higher order terms
  • 4.1. NLSE with third order dispersion, self-steepening, and self-frequency shift
  • 4.2. Summary of section 4.1
  • 4.3. Special cases of equation (4.1)
  • 4.4. NLSE with first and third order dispersions, self-steepening, self-frequency shift, and potential
  • 4.5. Summary of section 4.4
  • 4.6. NLSE with fourth order dispersion
  • 4.7. Summary of section 4.6
  • 4.8. NLSE with fourth order dispersion and power law nonlinearity
  • 4.9. Summary of section 4.8
  • 4.10. NLSE with third and fourth order dispersions and cubic and quintic nonlinearities
  • 4.11. Summary of section 4.10
  • 4.12. NLSE with third and fourth order dispersions, self-steepening, self-frequency shift, and cubic and quintic nonlinearities
  • 4.13. Summary of section 4.12
  • 4.14. NLSE with [pipe][psi][pipe]2-dependent dispersion
  • 4.15. Infinite hierarchy of integrable NLSEs with higher order terms
  • 4.16. Summary of section 4.15
  • 5. Scaling transformations
  • 5.1. Fundamental NLSE to fundamental NLSE with different constant coefficients
  • 5.2. Defocusing (focusing) NLSE to focusing (defocusing) NLSE
  • 5.3. Galilean transformation (movable solutions)
  • 5.4. Function coefficients
  • 5.5. Solution-dependent transformation
  • 5.6. Summary of sections 5.1-5.5
  • 5.7. Other equations : NLSE with periodic potentials
  • 5.8. Summary of section 5.7
  • 6. Nonlinear Schrödinger equation in (N + 1)-dimensions
  • 6.1. (N + 1)-dimensional NLSE with cubic nonlinearity
  • 6.2. (N + 1)-dimensional NLSE with power law nonlinearity
  • 6.3. (N + 1)-dimensional NLSE with dual power law nonlinearity
  • 6.4. Galilean Transformation in (N + 1)-dimensions (movable solutions)
  • 6.5. NLSE in (2 + 1)-Dimensions with [phi]x1x2 term
  • 6.6. Summary of sections 6.1-6.5
  • 6.7. (N + 1)-dimensional isotropic NLSE with cubic nonlinearity in polar coordinate system
  • 6.8. Summary of section 6.7
  • 6.9. Power series solutions to (2 + 1)-dimensional NLSE with cubic nonlinearity in a polar coordinate system
  • 7. Coupled nonlinear Schrödinger equations
  • 7.1. Fundamental coupled NLSE Manakov system
  • 7.2. Summary of section 7.1
  • 7.3. Symmetry reductions
  • 7.4. Scaling transformations
  • 7.5. Summary of sections 7.3-7.4
  • 7.6. (N + 1)-Dimensional coupled NLSE (N + 1)-dimensional Manakov system
  • 7.7. Symmetry reductions of (N + 1)-dimensional CNLSE to Scalar NLSE
  • 7.8. (N + 1)-dimensional scaling transformations
  • 7.9. Summary of sections 7.7-7.8
  • 8. Discrete nonlinear Schrödinger equation
  • 8.1. Discrete NLSE with saturable nonlinearity
  • 8.2. Summary of section 8.1
  • 8.3. Short-period solutions with general, Kerr, and saturable nonlinearities
  • 8.4. Ablowitz-Ladik equation
  • 8.5. Summary of section 8.4
  • 8.6. Cubic-quintic discrete NLSE
  • 8.7. Summary of section 8.6
  • 8.8. Generalized discrete NLSE
  • 8.9. Summary of section 8.8
  • 8.10. Coupled Salerno equations
  • 8.11. Summary of section 8.10
  • 8.12. Coupled Ablowitz-Ladik equation
  • 8.13. Summary of section 8.12
  • 8.14. Coupled saturable discrete NLSE
  • 8.15. Summary of section 8.14
  • 9. Nonlocal nonlinear Schrödinger equation
  • 9.1. Nonlocal NLSE
  • 9.2. Nonlocal coupled NLSE
  • 9.3. Symmetry reductions to scalar nonlocal NLSE
  • 9.4. Scaling transformations
  • 9.5. Nonlocal discrete NLSE with saturable nonlinearity
  • 9.6. Nonlocal Ablowitz-Ladik Equation
  • 9.7. Nonlocal cubic-quintic discrete NLSE
  • 9.8. Summary of chapter 9
  • Appendices. A. Derivation of some solutions of chapters 2 and 3
  • B. Darboux transformation single soliton and breather solutions
  • C. Derivation of the similarity transformations in chapter.

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