08565nam a2200769 i 4500 9780750359542 IOP 20251030124832.0 m eo d cr cn |||m|||a 241003s2024 enka fob 000 0 eng d 9780750359542 ebook 9780750359535 mobi 9780750359528 print 9780750359559 myPrint 10.1088/978-0-7503-5954-2 doi (CaBNVSL)thg00083989 (OCoLC)1458669174 CaBNVSL eng rda CaBNVSL CaBNVSL QC174.26.W28 K535 2024eb PHU bicssc SCI040000 bisacsh Khawaja, Usama Al, author. 97113 Handbook of exact solutions to the nonlinear Schr�odinger equations / Usama Al Khawaja, Laila Al Sakkaf. Second edition. Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2024] 1 online resource (various pagings) : illustrations (some color). text rdacontent electronic isbdmedia online resource rdacarrier [IOP release $release] IOP ebooks. [2024 collection] "Version: 20240901"--Title page verso. Includes bibliographical references. 1. Introduction -- 2. Fundamental nonlinear Schr�odinger equation -- 2.1. Introduction -- 2.2. NLSE with cubic nonlinearity 3. Nonlinear Schr�odinger equation with power law and dual power law nonlinearities -- 3.1. Introduction -- 3.2. NLSE with power law nonlinearity -- 3.3. Summary of section 3.2 -- 3.4. NLSE with dual power law nonlinearity -- 3.5. Summary of section 3.4 4. Nonlinear Schr�odinger equation with higher order terms -- 4.1. Introduction -- 4.2. NLSE with third order dispersion, self-steepening, and self-frequency shift -- 4.3. Summary of section 4.2 -- 4.4. Special cases of equation (4.17) -- 4.5. NLSE with first and third order dispersions, self-steepening, self-frequency shift, and potential -- 4.6. Summary of section 4.5 -- 4.7. NLSE with t-dependent coefficients and first order dispersion -- 4.8. Summary of section 4.7 -- 4.9. NLSE with fourth order dispersion -- 4.10. Summary of section 4.9 -- 4.11. NLSE with fourth order dispersion and power law nonlinearity -- 4.12. Summary of section 4.11 -- 4.13. NLSE with third and fourth order dispersions and cubic and quintic nonlinearities -- 4.14. Summary of section 4.13 -- 4.15. NLSE with third and fourth order dispersions, self-steepening, self-frequency shift, and cubic and quintic nonlinearities -- 4.16. Summary of section 4.15 -- 4.17. NLSE with y 2 | | -dependent dispersion -- 4.18. Infinite hierarchy of integrable NLSEs with higher order terms -- 4.19. Summary of section 4.18 5. Scaling transformations -- 5.1. Introduction -- 5.2. Fundamental NLSE to fundamental NLSE with different constant coefficients -- 5.3. Defocusing (focusing) NLSE to focusing (defocusing) NLSE -- 5.4. Galilean transformation (moving solutions) -- 5.5. Function coefficients -- 5.6. Solution-dependent transformation -- 5.7. Summary of sections 5.2-5.6 -- 5.8. Other equations -- 5.9. Summary of section 5.8 6. Nonlinear Schr�odinger equation in (N + 1)-dimensions -- 6.1. Introduction -- 6.2. (N + 1)-dimensional NLSE with cubic nonlinearity -- 6.3. (N + 1)-dimensional NLSE with power law nonlinearity -- 6.4. (N + 1)-dimensional NLSE with dual power law nonlinearity -- 6.5. Galilean transformation in (N + 1)-dimensions (moving solutions) -- 6.6. NLSE in (2 + 1)-dimensions with [phi]x x1 2 term -- 6.7. Summary of sections 6.2-6.6 -- 6.8. (N + 1)-dimensional isotropic NLSE with cubic nonlinearity in polar coordinate system -- 6.9. Summary of section 6.8 -- 6.10. Power series solutions to (2 + 1)-dimensional NLSE with cubic nonlinearity in polar coordinate system 7. Coupled nonlinear Schr�odinger equations -- 7.1. Introduction -- 7.2. Fundamental coupled NLSE Manakov system -- 7.3. Summary of section 7.2 -- 7.4. Symmetry seductions -- 7.5. Scaling transformations -- 7.6. Summary of sections 7.4-7.5 -- 7.7. (N + 1)-dimensional coupled NLSE (N + 1)-dimensional Manakov system -- 7.8. Symmetry reductions of (N + 1)-dimensional cNLSE to scalar NLSE -- 7.9. (N + 1)-dimensional scaling transformations -- 7.10. Composite solutions: nonlinear superposition -- 7.11. Summary of sections 7.8-7.10 8. Discrete nonlinear Schr�odinger equation -- 8.1. Introduction -- 8.2. Discrete NLSE with saturable nonlinearity -- 8.3. Summary of section 8.2 -- 8.4. Short-period solutions with general, Kerr, and saturable nonlinearities -- 8.5. ABLOWITZ-LADIK equation -- 8.6. Summary of section 8.5 -- 8.7. Cubic-quintic discrete NLSE -- 8.8. Summary of section 8.7 -- 8.9. Generalized discrete NLSE -- 8.10. Summary of section 8.9 -- 8.11. Coupled Salerno equations -- 8.12. Summary of section 8.11 -- 8.13. Coupled Ablowitz-Ladik equation -- 8.14. Summary of section 8.13 -- 8.15. Coupled saturable discrete NLSE -- 8.16. Summary of section 8.15 9. Nonlocal nonlinear Schr�odinger equation -- 9.1. Introduction -- 9.2. Nonlocal NLSE -- 9.3. Yang's nonlocal NLSE -- 9.4. Nonlocal coupled NLSE -- 9.5. Symmetry reductions to scalar nonlocal NLSE -- 9.6. Scaling transformations -- 9.7. Nonlocal discrete NLSE with saturable nonlinearity -- 9.8. Nonlocal Ablowitz-Ladik equation -- 9.9. Nonlocal cubic-quintic discrete NLSE -- 9.10. Summary of chapter 9 10. Fractional nonlinear Schr�odinger equation -- 10.1. Introduction -- 10.2. Conformable fractional derivative -- 10.3. Summary of section 10.2 -- 10.4. Fractal fractional derivative -- 10.5. Summary of section 10.4 -- 10.6. Atangana ([beta]) fractional derivative -- 10.7. Summary of section 10.6 Appendix A. Derivation of some solutions of chapters 2 and 3 -- Appendix B. Darboux transformation: single soliton and breather solutions -- Appendix C. Derivation of the similarity transformations in chapter 5. Full-text restricted to subscribers or individual document purchasers. Throughout the long history of the nonlinear Schr�odinger equation (NLSE), many exact analytical solutions have been found and they continue to grow as new solutions are being sought and discovered. This book aims to organize the solutions by classifying and grouping them based on aspects and symmetries they possess. The authors present a systematic derivation of many solutions and even include new derivations. This expanded second edition contains new solutions published or derived since the first edition. Noting the increasing interest in and applications of the fractional nonlinear Schr�odinger equation, a new chapter devoted to this topic has been added. Each chapter now also features an introductory section documenting the history, background, and physical systems described by the equations at hand. Professional and scholarly. Also available in print. Mode of access: World Wide Web. System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader. Usama Al Khawaja is a theoretical Physicist who is currently a full professor in the Department of Physics at the University of Jordan. He is specialized in solitons and their applications, exact solutions and methods of solution. Laila Al Sakkaf is currently an assistant professor in the College of Engineering at Abu Dhabi University. She is specialized in solitons and their applications, exact solutions and methods of solution. Title from PDF title page (viewed on October 3, 2024). Schr�odinger equation. 97114 Differential equations, Nonlinear. 97115 Nonlinear wave equations. 97116 Mathematical physics. bicssc SCIENCE / Physics / Mathematical & Computational. bisacsh 96672 Sakkaf, Laila Al, author. 97117 Institute of Physics (Great Britain), publisher. 17702 Print version: 9780750359528 9780750359559 IOP (Series). Release 24. IOP ebooks. 2024 collection. https://iopscience.iop.org/book/mono/978-0-7503-5954-2 E-Books 68519 68519