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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :
IOP Publishing,
[2020]
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| Colección: | IOP ebooks. 2020 collection.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 050 | 4 | |a QC174.26.W28 |b K535 2020eb | |
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| 072 | 7 | |a SCI040000 |2 bisacsh | |
| 082 | 0 | 4 | |a 530.124 |2 23 |
| 100 | 1 | |a Khawaja, Usama, |e author. | |
| 245 | 1 | 0 | |a Handbook of exact solutions to the nonlinear Schrödinger equations / |c Usama Al Khawaja and Laila Al Sakkaf. |
| 264 | 1 | |a Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : |b IOP Publishing, |c [2020] | |
| 300 | |a 1 online resource (various pagings) : |b illustrations (some color). | ||
| 336 | |a text |2 rdacontent | ||
| 337 | |a electronic |2 isbdmedia | ||
| 338 | |a online resource |2 rdacarrier | ||
| 490 | 1 | |a IOP ebooks. [2020 collection] | |
| 500 | |a "Version: 20191101"--Title page verso. | ||
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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. | |
| 520 | 3 | |a 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 elsewhere using various methods, the authors present a systematic derivation of many solutions and even include new derivations. They have also presented symmetries and reductions that connect different solutions through transformations and enable classifying new solutions into known classes. For the user to verify that the presented solutions do satisfy the NLSE, this monumental work is accompanied by Mathematica Notebooks containing all solutions. This work also features a large number of figures, and animations are included to help visualize solutions and their dynamics. | |
| 521 | |a Researchers across a range of physics disciplines, as well as engineers and chemists. | ||
| 530 | |a Also available in print. | ||
| 538 | |a Mode of access: World Wide Web. | ||
| 538 | |a System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader. | ||
| 545 | |a Usama Al Khawaja obtained his Bachelor's degree in Physics from the University of Jordan in 1992 and Master's degree in Physics from the University of Jordan in 1996. He earned his PhD degree in theoretical Physics from the University of Copenhagen in 1999. He spent three years of postdoctoral research at Utrecht University in the Netherlands before joining the United Arab Emirates University in 2002 as an assistant professor. He is currently a full professor and Chairman of the Physics department at the United Arab Emirates University. His main areas of research are Bose-Einstein condensation, nonlinear and quantum optics, integrability and exact solutions. His main achievements in integrability and exact solutions include developing a systematic search method of finding Lax pairs of a given nonlinear partial differential equation. He also developed a convergent power series method for solving nonlinear differential equations. He has authored more than 70 papers and obtained one patent on applying discrete solitons in all-optical operations. Laila Al Sakkaf obtained her Bachelor's degree in Physics from the United Arab Emirates University in 2015 and her Master's degree in Physics from the United Arab Emirates University in 2018. She is currently a research assistant and a PhD student at the Physics department of the United Arab Emirates University. Her current research focus is on integrability and exact solutions of differential equations modeling nonlinear physical phenomena. | ||
| 588 | 0 | |a Title from PDF title page (viewed on December 9, 2019). | |
| 650 | 0 | |a Schrödinger equation. | |
| 650 | 0 | |a Differential equations, Nonlinear. | |
| 650 | 0 | |a Nonlinear wave equations. | |
| 650 | 7 | |a Mathematical physics. |2 bicssc | |
| 650 | 7 | |a SCIENCE / Physics / Mathematical & Computational. |2 bisacsh | |
| 700 | 1 | |a Sakkaf, Laila, |e author. | |
| 710 | 2 | |a Institute of Physics (Great Britain), |e publisher. | |
| 776 | 0 | 8 | |i Print version: |z 9780750324267 |
| 830 | 0 | |a IOP ebooks. |p 2020 collection. | |
| 856 | 4 | 0 | |u https://iopscience.uam.elogim.com/book/978-0-7503-2428-1 |z Texto completo |